Chapter 2: Describing Motion: Kinematics In One Dimension

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1. A car travels 90 km/h. How long does it take for it to travel 400 km?

Explanation

The car is traveling at a speed of 90 km/h. To find the time it takes for the car to travel 400 km, we divide the distance by the speed. 400 km divided by 90 km/h equals approximately 4.4 hours. Therefore, it takes the car 4.4 hours to travel 400 km.

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About This Quiz
Kinematics Quizzes & Trivia

This quiz in 'Chapter 2: Describing Motion: Kinematics in One Dimension' assesses understanding of motion concepts such as displacement, velocity, and acceleration in physics. It focuses on practical scenarios to illustrate these fundamental principles, enhancing both theoretical and practical knowledge.

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2. Ball A is dropped from the top of a building. One second later, ball B is dropped from the same building. As time progresses, the difference in their speeds

Explanation

The explanation for the correct answer "remains constant" is that both balls are dropped from the same building, which means they experience the same acceleration due to gravity. This acceleration remains constant throughout the motion, regardless of the time at which the balls were dropped. Therefore, the difference in their speeds will remain constant as well.

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3. An airplane increases its speed from 100 m/s to 160 m/s, at the average rate of 15 m/s^2. How much time does it take for the complete increase in speed?

Explanation

The airplane increases its speed from 100 m/s to 160 m/s, a difference of 60 m/s. The average rate of increase is given as 15 m/s^2. Using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange the formula to solve for t. Plugging in the values, we have 160 = 100 + 15t. Solving for t, we get t = 4.0 seconds. Therefore, it takes 4.0 seconds for the complete increase in speed.

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4. An object is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s^2. How long does it take for the object to reach the maximum height?

Explanation

The time it takes for an object to reach its maximum height when thrown upwards can be calculated using the formula: t = v/g, where v is the initial velocity and g is the acceleration due to gravity. In this case, the initial velocity is 12 m/s and the acceleration due to gravity on planet X is 1.5 m/s^2. Plugging these values into the formula, we get t = 12 m/s / 1.5 m/s^2 = 8.0 s. Therefore, it takes 8.0 seconds for the object to reach its maximum height.

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5. When is the average velocity of an object equal to the instantaneous velocity?

Explanation

The average velocity of an object is equal to the instantaneous velocity only when the velocity is constant. This means that the object is moving at a consistent speed and in a straight line without any changes in direction. In such cases, the average velocity over a given time interval will be the same as the velocity at any specific moment within that interval. However, if the velocity is changing, either in magnitude or direction, the average velocity will not be equal to the instantaneous velocity.

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6. 55 mi/h is how many m/s? (1 mi = 1609 m.)

Explanation

To convert miles per hour (mi/h) to meters per second (m/s), we need to multiply the given value by a conversion factor. The conversion factor is 1609 m/1 mi since 1 mile is equal to 1609 meters. By multiplying 55 mi/h by the conversion factor, we get 55 mi/h * 1609 m/1 mi = 88,495 m/h. To convert this to m/s, we need to divide by 3600 (since there are 3600 seconds in an hour). Therefore, 88,495 m/h / 3600 s/h = 24.58 m/s, which can be rounded to 25 m/s.

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7. An object moving in the +x axis experiences an acceleration of 2.0 m/s^2. This means the object is

Explanation

The given information states that the object is experiencing an acceleration of 2.0 m/s^2. Acceleration is the rate of change of velocity, so if the object is experiencing an acceleration of 2.0 m/s^2, it means its velocity is increasing by 2.0 m/s every second. Therefore, the correct answer is "increasing its velocity by 2.0 m/s in every second."

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8. A car goes from 40 m/s to 80 m/s in a distance of 200 m. What is its average acceleration?

Explanation

The average acceleration of an object can be calculated using the formula: average acceleration = (final velocity - initial velocity) / time. However, in this question, the time is not given. Instead, the distance is provided. To solve this, we can use the formula: average acceleration = (final velocity^2 - initial velocity^2) / (2 * distance). Plugging in the values, we get (80^2 - 40^2) / (2 * 200) = 12 m/s^2. Therefore, the correct answer is 12 m/s^2.

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9. Suppose a ball is thrown straight up. Make a statement about the velocity and the acceleration when the ball reaches the highest point.

Explanation

When the ball reaches the highest point, its velocity is zero because it momentarily stops moving before it starts falling back down. However, its acceleration is not zero because gravity is still acting on the ball, pulling it downwards. The acceleration due to gravity is constant and always acts in the downward direction, even when the ball is at its highest point.

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10. Suppose a ball is thrown straight up, reaches a maximum height, then falls to its initial height. Make a statement about the direction of the velocity and acceleration as the ball is going up.

Explanation

As the ball is going up, its velocity points upward because it is moving in the opposite direction of gravity. However, its acceleration points downward because gravity is constantly pulling it downward, causing it to slow down and eventually reverse direction. Therefore, the correct answer is that its velocity points upward and its acceleration points downward.

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11. The slope of a position versus time graph gives

Explanation

The slope of a position versus time graph represents the rate at which an object's position is changing over time. This rate is known as velocity, which is the speed and direction of an object's motion. Therefore, the correct answer is velocity.

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12. The slope of a velocity versus time graph gives

Explanation

The slope of a velocity versus time graph gives the rate of change of velocity, which is acceleration. This is because acceleration is defined as the change in velocity per unit time. Therefore, the correct answer is acceleration.

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13. Suppose that an object is moving with a constant velocity. Make a statement concerning its acceleration.

Explanation

If an object is moving with a constant velocity, it means that its speed and direction are not changing. In order for acceleration to be present, there must be a change in velocity. Since the object's velocity is not changing, the acceleration must be equal to zero.

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14. An object is moving with constant non-zero velocity in the +x axis. The position versus time graph of this object is

Explanation

The correct answer is a straight line making an angle with the time axis. When an object is moving with constant non-zero velocity in the +x axis, its position versus time graph will be a straight line. The angle that this straight line makes with the time axis represents the velocity of the object.

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15. An object is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s^2. What is the maximum height reached by the object?

Explanation

The maximum height reached by the object can be determined using the kinematic equation for vertical motion. The equation is given by:

h = (v^2 - u^2) / (2g)

Where h is the maximum height, v is the final velocity (0 m/s at the highest point), u is the initial velocity (12 m/s), and g is the acceleration due to gravity (1.5 m/s^2).

Plugging in the values, we get:

h = (0^2 - 12^2) / (2 * 1.5)
h = (-144) / 3
h = -48 m

Since height cannot be negative, the maximum height reached by the object is 48 m.

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16. Suppose that an object travels from one point in space to another. Make a comparison between the displacement and the distance traveled.

Explanation

The displacement is either less than or equal to the distance traveled because displacement refers to the change in position from the starting point to the ending point, regardless of the path taken. The distance traveled, on the other hand, refers to the total length of the path taken. In some cases, the displacement may be less than the distance traveled if the object takes a longer route or changes direction multiple times. However, it can also be equal to the distance traveled if the object travels in a straight line from start to finish.

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17. Two objects are thrown from the top of a tall building. One is thrown up, and the other is thrown down, both with the same initial speed. What are their speeds when they hit the street?

Explanation

The two objects have the same initial speed, so they will experience the same acceleration due to gravity as they fall towards the ground. This means that their speeds will be the same when they hit the street. The height of the building is not relevant in determining their speeds, as it only affects the time it takes for them to reach the ground.

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18. A brick is dropped from the top of a building. A second brick is thrown straight down from the same building. They are released at the same time. Neglect air resistance. Compare the accelerations of the two bricks.

Explanation

The acceleration of an object in free fall near the surface of the Earth is constant and equal to the acceleration due to gravity, which is approximately 9.8 m/s^2. Since both bricks are released at the same time and neglecting air resistance, they will experience the same acceleration due to gravity. Therefore, the correct answer is that the two bricks accelerate at the same rate.

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19. An object moves 15.0 m north and then 11.0 m south. Find both the distance traveled and the magnitude of the displacement vector.

Explanation

The distance traveled is the sum of the distances traveled in each direction, which is 15.0 m + 11.0 m = 26.0 m. The magnitude of the displacement vector is the straight-line distance between the starting point and the ending point, which is the absolute value of the difference between the distances traveled in each direction, which is |15.0 m - 11.0 m| = 4.0 m. Therefore, the correct answer is 26.0 m, 6.0 m.

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20. What must be your average speed in order to travel 350 km in 5.15 h?

Explanation

To calculate average speed, we divide the total distance traveled by the total time taken. In this case, the total distance is 350 km and the total time is 5.15 hours. Dividing 350 by 5.15 gives us approximately 67.96 km/h. Since speed is usually rounded to the nearest whole number, the correct answer is 68.0 km/h.

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21. In a 400-m relay race the anchorman (the person who runs the last 100 m) for team A can run 100 m in 9.8 s. His rival, the anchorman for team B, can cover 100 m in 10.1 s. What is the largest lead the team B runner can have when the team A runner starts the final leg of the race, in order that the team A runner not lose the race?

Explanation

The team A runner can cover 100 m in 9.8 seconds, while the team B runner can cover the same distance in 10.1 seconds. To calculate the largest lead the team B runner can have, we need to find the time it takes for the team A runner to cover 100 m. Since the team A runner is the anchorman, they will start running after the other team has already started. So, the team B runner will have a head start equal to the time it takes for the team A runner to cover 100 m. The difference in time is 10.1 - 9.8 = 0.3 seconds. Using the formula speed = distance/time, we can calculate the distance covered by the team B runner in 0.3 seconds, which is 0.3 * 10 = 3.0 meters. Therefore, the largest lead the team B runner can have is 3.0 meters.

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22. Suppose that a car traveling to the East (+x direction) begins to slow down as it approaches a traffic light. Make a statement concerning its acceleration.

Explanation

The given statement indicates that the car is slowing down, which means its velocity is decreasing. Since acceleration is the rate of change of velocity, a negative acceleration is required to cause a decrease in velocity. Therefore, the correct answer is that the car is decelerating, and its acceleration is negative.

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23. Objects A and B both start at rest. They both accelerate at the same rate. However, object A accelerates for twice the time as object B. What is the final speed of object A compared to that of object B?

Explanation

Since both objects accelerate at the same rate, the final speed of an object is directly proportional to the time it accelerates. In this case, object A accelerates for twice the time as object B. Therefore, object A will have twice the final speed compared to object B.

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24. Suppose a ball is thrown straight up. What is its acceleration just before it reaches its highest point?

Explanation

The acceleration of the ball just before it reaches its highest point is exactly g. This is because at the highest point of its trajectory, the ball momentarily comes to a stop before reversing its direction and falling back down. At this point, the acceleration due to gravity is the only force acting on the ball, pulling it back towards the ground at a constant rate of g, which is approximately 9.8 m/s^2.

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25. A runner ran the marathon (approximately 42.0 km) in 2 hours and 57 min. What is the average speed of the runner in m/s?

Explanation

The average speed of the runner can be calculated by dividing the total distance covered by the time taken. In this case, the runner covered a distance of approximately 42.0 km, which is equal to 42,000 meters. The time taken was 2 hours and 57 minutes, which is equal to 177 minutes. To convert this to seconds, we multiply by 60, giving us 10,620 seconds. Dividing the distance by the time, we get an average speed of approximately 3.95 m/s.

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26. A ly (light year) is the distance that light travels in one year. The speed of light is 3.00 * 10^8 m/s. How many miles are there in a ly? (1 mi = 1609 m, 1 yr = 365 d.)

Explanation

The speed of light is given as 3.00 * 10^8 m/s. To find the distance in miles, we need to convert this speed from meters to miles. We know that 1 mile is equal to 1609 meters. Therefore, we can calculate the distance in miles by dividing the speed of light in meters by 1609.

3.00 * 10^8 m/s / 1609 m = 1.86 * 10^5 mi/s

Next, we need to find the distance traveled in one year. We know that there are 365 days in a year. Therefore, we can multiply the speed in miles per second by the number of seconds in a day (24 hours * 60 minutes * 60 seconds) and then multiply by 365.

1.86 * 10^5 mi/s * (24 * 60 * 60) s/day * 365 days/year = 5.88 * 10^12 mi

Therefore, the correct answer is 5.88 * 10^12 mi.

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27. An airplane travels at 300 mi/h south for 2.00 h and then at 250 mi/h north for 750 miles. What is the average speed for the trip?

Explanation

The average speed for the trip can be calculated by finding the total distance traveled and dividing it by the total time taken. The airplane travels 300 mi/h south for 2.00 h, covering a distance of 600 miles. Then it travels at 250 mi/h north for 750 miles. The total distance traveled is 600 + 750 = 1350 miles. The total time taken is 2.00 h + (750/250) h = 5.00 h. Therefore, the average speed for the trip is 1350 miles / 5.00 hours = 270 mi/h.

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28. Suppose a ball is thrown downward in the absence of air resistance. Make a statement concerning its acceleration.

Explanation

In the absence of air resistance, the only force acting on the ball is gravity. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since the mass of the ball remains constant and the force of gravity is constant, the acceleration of the ball remains constant as well. Therefore, the correct statement is that its acceleration is constant.

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29. A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, then 1.0 km north, then 1.0 km west to return to its starting point. This trip takes 45 min. What was the bear's average speed?

Explanation

The polar bear traveled a total distance of 4.0 km (1.0 km south + 1.0 km east + 1.0 km north + 1.0 km west). Since the trip took 45 minutes, we need to convert the time to hours by dividing it by 60. Therefore, the average speed of the bear is calculated by dividing the distance (4.0 km) by the time (45/60 hours), which equals 5.3 km/h.

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30. A motorist travels 160 km at 80 km/h and 160 km at 100 km/h. What is the average speed of the motorist for this trip?

Explanation

The average speed of a trip is calculated by dividing the total distance traveled by the total time taken. In this case, the motorist travels a total distance of 320 km (160 km + 160 km) and the total time taken is 4 hours (160 km / 80 km/h + 160 km / 100 km/h = 2 hours + 1.6 hours = 3.6 hours). Dividing the total distance by the total time gives us an average speed of approximately 89 km/h.

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31. A car travels at 15 m/s for 10 s. It then speeds up with a constant acceleration of 2.0 m/s^2 for 15 s. At the end of this time, what is its velocity?

Explanation

The car initially travels at a constant velocity of 15 m/s for 10 seconds. This means that its final velocity at the end of this time is still 15 m/s. However, after 10 seconds, the car starts to accelerate with a constant acceleration of 2.0 m/s^2 for 15 seconds. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the final velocity as follows: v = 15 + 2.0 * 15 = 45 m/s. Therefore, the correct answer is 45 m/s.

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32. A cart with an initial velocity of 5.0 m/s experiences a constant acceleration of 2.0 m/s2. What is the cart's displacement during the first 6.0 s of its motion?

Explanation

Given that the cart has an initial velocity of 5.0 m/s and experiences a constant acceleration of 2.0 m/s^2, we can use the equation of motion: displacement = initial velocity * time + (1/2) * acceleration * time^2. Plugging in the values, we get: displacement = 5.0 * 6.0 + (1/2) * 2.0 * (6.0)^2 = 30 + 36 = 66 m. Therefore, the cart's displacement during the first 6.0 s of its motion is 66 m.

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33. The area under a curve in an acceleration versus time graph gives

Explanation

The area under a curve in an acceleration versus time graph gives the change in velocity. This is because acceleration is the rate of change of velocity, so integrating the acceleration over time gives the change in velocity. Therefore, the correct answer is velocity.

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34. If the velocity versus time graph of an object is a straight line making an angle of 30 degrees with the time axis, the object is

Explanation

If the velocity versus time graph of an object is a straight line making an angle of 30 degrees with the time axis, it indicates that the object is moving with a constant non-zero acceleration. This is because the slope of the velocity versus time graph represents the acceleration of the object. Since the graph is a straight line, it means that the acceleration is constant. Additionally, the fact that the line makes an angle of 30 degrees with the time axis suggests that the acceleration is non-zero.

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35. An object is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s^2. How long does it take for the object to return to where it is thrown?

Explanation

The object is thrown upward with an initial velocity of 15 m/s. Since the acceleration due to gravity on planet X is 2.5 m/s^2, the object will experience a deceleration as it moves against the direction of gravity. The object will eventually reach its maximum height and start falling back down. The time it takes for the object to reach its maximum height can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 0 m/s (at maximum height), the initial velocity is 15 m/s, and the acceleration is -2.5 m/s^2 (opposite direction to the initial velocity). Solving for time, we get t = (v - u) / a = (0 - 15) / -2.5 = 6 s. Since the object takes the same amount of time to come back down as it took to reach the maximum height, the total time for the object to return to where it was thrown is 6 s + 6 s = 12 s.

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36. A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, then 1.0 km north, then 1.0 km west to return to its starting point. This trip takes 45 min. What was the bear's average velocity?

Explanation

The bear's average velocity is 0 km/h because it returns to its starting point, which means it has no displacement. Velocity is defined as the rate of change of displacement, so if there is no displacement, the velocity is 0.

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37. A cart starts from rest and accelerates at 4.0 m/s2 for 5.0 s, then maintain that velocity for 10 s, and then decelerates at the rate of 2.0 m/s2 for 4.0 s. What is the final speed of the car?

Explanation

The cart starts from rest and accelerates at 4.0 m/s2 for 5.0 s, which means its velocity increases by 4.0 m/s every second for 5 seconds. Therefore, the cart's velocity after the acceleration phase is 4.0 m/s * 5 s = 20 m/s.

After the acceleration phase, the cart maintains that velocity for 10 s, so its final velocity remains at 20 m/s.

Finally, the cart decelerates at a rate of 2.0 m/s2 for 4.0 s, which means its velocity decreases by 2.0 m/s every second for 4 seconds. Therefore, the cart's velocity after the deceleration phase is 20 m/s - (2.0 m/s * 4 s) = 20 m/s - 8 m/s = 12 m/s.

Thus, the final speed of the cart is 12 m/s.

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38. Can an object's velocity change direction when its acceleration is constant? Support your answer with an example.

Explanation

The correct answer is "Yes, this is possible, and a rock thrown straight up is an example." This is because when a rock is thrown straight up, its velocity changes direction while its acceleration remains constant. Initially, the rock is accelerating upwards due to the force applied to it. As it reaches its maximum height, the velocity becomes zero, and then it starts accelerating downwards due to the force of gravity. Therefore, even though the acceleration remains constant, the velocity changes direction.

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39. An object is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s^2. What is the speed of the object after 8.0 s?

Explanation

The speed of the object after 8.0 s will be 14 m/s. This is because the object is thrown upward with an initial speed of 14 m/s, and the acceleration due to gravity on planet X is 3.5 m/s^2. Since the object is thrown upward, the acceleration due to gravity will act against its motion, causing its speed to decrease. However, after 8.0 s, the object will have reached its highest point and started to fall back down. At this point, its speed will be equal to its initial speed of 14 m/s.

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40. When an object is released from rest and falls in the absence of friction, which of the following is true concerning its motion?

Explanation

When an object is released from rest and falls in the absence of friction, its acceleration is constant. This is because the only force acting on the object is gravity, which causes a constant acceleration towards the ground. The velocity of the object increases continuously as it falls, but its acceleration remains constant throughout the motion.

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41. If you are driving 72 km/h along a straight road and you look to the side for 4.0 s, how far do you travel during this inattentive period?

Explanation

When driving at a constant speed of 72 km/h, the distance traveled can be calculated by multiplying the speed by the time. In this case, the time is given as 4.0 seconds. To convert the speed from km/h to m/s, divide it by 3.6. So, 72 km/h is equal to 20 m/s. Multiplying the speed by the time gives us 20 m/s * 4 s = 80 m. Therefore, during the 4.0-second period of inattention, the driver travels a distance of 80 meters.

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42. A ball is thrown upward at a velocity of 19.6 m/s. What is its velocity after 3.00 s?

Explanation

The correct answer is 9.8 m/s downward because when a ball is thrown upward, its velocity decreases due to the force of gravity. After 3.00 seconds, the ball would have reached its maximum height and started to fall back down. At this point, its velocity would be equal to the acceleration due to gravity, which is 9.8 m/s downward.

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43. A new car manufacturer advertises that their car can go "from zero to sixty in 8 s". This is a description of

Explanation

The statement "from zero to sixty in 8 s" describes the average acceleration of the car. Average acceleration is calculated by dividing the change in velocity (from zero to sixty) by the time taken (8 seconds). This description indicates how quickly the car can increase its velocity over a specific time interval, which is average acceleration.

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44. Suppose a can, after an initial kick, moves up along a smooth hill of ice. Make a statement concerning its acceleration.

Explanation

The correct answer is that the can will have the same acceleration, both up the hill and down the hill. This is because acceleration is determined by the net force acting on an object, and in this case, the only force acting on the can is gravity. Since gravity acts in the same direction regardless of whether the can is moving up or down the hill, the acceleration remains constant.

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45. A ball is thrown vertically upward with a speed v. An identical second ball is thrown upward with a speed 2v (twice as fast). What is the ratio of the maximum height of the second ball to that of the first ball? (How many times higher does the second ball go than the first ball?)

Explanation

The ratio of the maximum height of the second ball to that of the first ball is 4:1. This is because the maximum height reached by a vertically thrown ball is directly proportional to the square of its initial velocity. Since the second ball is thrown with twice the initial velocity of the first ball, its maximum height will be four times higher than that of the first ball. Therefore, the ratio is 4:1.

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46. An object is moving in a straight line with constant acceleration. Initially it is traveling at 16 m/s. Three seconds later it is traveling at 10 m/s. How far does it move during this time?

Explanation

The object is moving with a constant acceleration, which means its velocity is changing at a constant rate. From the given information, we can calculate the acceleration by subtracting the initial velocity (16 m/s) from the final velocity (10 m/s), and dividing it by the time taken (3 seconds). This gives us an acceleration of -2 m/s^2 (negative because the velocity is decreasing).

Using the equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can find the displacement (distance) traveled by the object during this time. Plugging in the values, we get 10 m/s = 16 m/s + (-2 m/s^2) * t. Solving for t, we get t = 3 seconds.

Now, we can use the equation of motion, s = ut + (1/2)at^2, where s is the displacement, to find the distance traveled. Plugging in the values, we get s = 16 m/s * 3 s + (1/2) * (-2 m/s^2) * (3 s)^2. Simplifying, we get s = 48 m - 9 m = 39 m. Therefore, the object moves 39 m during this time.

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47. You are driving home on a weekend from school at 55 mi/h for 110 miles. It then starts to snow and you slow to 35 mi/h. You arrive home after driving 4 hours and 15 minutes. How far is your hometown from school?

Explanation

Based on the given information, the total time taken to drive from school to home is 4 hours and 15 minutes. Since the speed changes from 55 mi/h to 35 mi/h, it is reasonable to assume that the time taken to cover the first 110 miles is less than the time taken to cover the remaining distance. Therefore, the distance between the hometown and school can be calculated by subtracting the time taken to cover the first 110 miles from the total time, and then multiplying it by the speed of 35 mi/h. This gives us (4 hours and 15 minutes - the time taken to cover the first 110 miles) * 35 mi/h, which equals 190 miles. So, the distance between the hometown and school is 190 miles.

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48. If the velocity of an object is zero, does it mean that the acceleration is zero? Support your answer with an example.

Explanation

The correct answer is no. When the velocity of an object is zero, it does not necessarily mean that the acceleration is zero. An example that supports this is an object starting from rest. In this case, the object initially has zero velocity, but it experiences an acceleration to increase its velocity over time. Therefore, the velocity is zero, but the acceleration is not.

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49. A jet fighter plane is launched from a catapult on an aircraft carrier. It reaches a speed of 42 m/s at the end of the catapult, and this requires 2.0 s. Assuming the acceleration is constant, what is the length of the catapult?

Explanation

The length of the catapult can be determined using the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken. In this case, the final velocity is 42 m/s, the initial velocity is 0 m/s (since the plane starts from rest), the time taken is 2.0 s, and the acceleration is constant. Plugging these values into the equation, we get 42 = 0 + a * 2.0. Solving for a, we find that the acceleration is 21 m/s^2. Now, using the equation s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time taken, we can find the distance traveled. Plugging in the values, we get s = 0 * 2.0 + (1/2) * 21 * (2.0)^2 = 0 + 21 * 2.0 = 42 m. Therefore, the length of the catapult is 42 m.

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50. An object is moving with constant non-zero velocity in the +x axis. The velocity versus time graph of this object is

Explanation

The object is moving with constant non-zero velocity in the +x axis, which means its velocity does not change over time. This is represented by a horizontal straight line on the velocity versus time graph. Since the velocity is constant, there is no acceleration, and therefore the graph does not show any change in velocity over time.

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51. The area under a curve in a velocity versus time graph gives

Explanation

The area under a curve in a velocity versus time graph represents the change in position or displacement. This is because the area under the curve represents the total distance traveled by an object over a certain time period. Since displacement is the change in position, it is the most appropriate interpretation of the area under the curve in this context. Acceleration, velocity, and position are not directly related to the area under the curve in a velocity versus time graph.

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52. If the position versus time graph of an object is a horizontal line, the object is

Explanation

If the position versus time graph of an object is a horizontal line, it means that the object is not changing its position over time. This indicates that the object is at rest, as it is not moving in any direction.

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53. Suppose that an object is moving with constant acceleration. Make a statement concerning its motion with respect to time.

Explanation

The correct answer is "In equal times its velocity changes by equal amounts." This statement is true because when an object is moving with constant acceleration, its velocity changes by the same amount in equal time intervals. This means that the object's speed increases or decreases at a constant rate over time.

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54. Suppose a skydiver jumps from a high-flying plane. What is her acceleration when she she reaches terminal velocity?

Explanation

When a skydiver reaches terminal velocity, it means that the force of gravity pulling her downward is balanced by the air resistance pushing upward. At this point, the net force on the skydiver is zero, which means there is no acceleration. Therefore, her acceleration when she reaches terminal velocity is essentially zero.

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55. A car starting from rest moves with constant acceleration of 2.0 m/s^2 for 10 s, then travels with constant speed for another 10 s, and then finally slows to a stop with constant acceleration of -2.0 m/s^2. How far does it travel?

Explanation

The car starts from rest and accelerates at a constant rate of 2.0 m/s^2 for 10 seconds. Using the formula s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration, we can calculate the distance traveled during this period to be 100 m.

After reaching this distance, the car travels with a constant speed for another 10 seconds. Since the speed is constant, the distance traveled during this period is simply the product of the speed and time, which is 2.0 m/s * 10 s = 20 m.

Finally, the car slows down with a constant acceleration of -2.0 m/s^2 until it comes to a stop. Using the same formula as before, we can calculate the distance traveled during this period to be 100 m.

Adding up the distances traveled during each period, we get a total distance of 100 m + 20 m + 100 m = 220 m. Therefore, the correct answer is 400 m.

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56. A motorist travels for 3.0 h at 80 km/h and 2.0 h at 100 km/h. What is her average speed for the trip?

Explanation

The average speed for a trip can be calculated by dividing the total distance traveled by the total time taken. In this case, the motorist travels for 3.0 hours at 80 km/h, covering a distance of 240 km, and for 2.0 hours at 100 km/h, covering a distance of 200 km. The total distance traveled is 240 km + 200 km = 440 km. The total time taken is 3.0 hours + 2.0 hours = 5.0 hours. Therefore, the average speed for the trip is 440 km / 5.0 hours = 88 km/h.

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57. When an object is released from rest and falls in the absence of friction, which of the following is true concerning its motion?

Explanation

The correct answer is None of the above is true. When an object is released from rest and falls in the absence of friction, the speed of the falling object is not proportional to its mass or weight. The speed of the falling object is also not inversely proportional to its surface area. In reality, in the absence of friction, all objects fall at the same rate regardless of their mass or weight, which is known as the principle of equivalence. This is explained by the gravitational force acting on the object being independent of its mass or weight.

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58. Under what condition is average velocity equal to the average of the object's initial and final velocity?

Explanation

When the acceleration is constant, the average velocity of an object over a certain time interval is equal to the average of its initial and final velocity. This is because when the acceleration is constant, the object's velocity changes at a constant rate. Therefore, the average velocity can be calculated by taking the average of the initial and final velocity.

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59. A ball is thrown straight up with a speed of 36.0 m/s. How long does it take to return to its starting point?

Explanation

When a ball is thrown straight up, it will reach its highest point and then fall back down to its starting point. The time it takes for the ball to reach its highest point is equal to the time it takes for it to fall back down to its starting point. Therefore, to find the total time it takes for the ball to return to its starting point, we can double the time it takes for it to reach its highest point. The time it takes for the ball to reach its highest point can be found using the equation v = u + at, where v is the final velocity (0 m/s at the highest point), u is the initial velocity (36.0 m/s), a is the acceleration (due to gravity, -9.8 m/s^2), and t is the time. Rearranging the equation to solve for t, we have t = (v - u) / a. Plugging in the values, we get t = (0 - 36.0) / -9.8 = 3.67 s. Doubling this value gives us the total time it takes for the ball to return to its starting point, which is 7.35 s. Therefore, the correct answer is 7.35 s.

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60. Suppose that a car traveling to the West (-x direction) begins to slow down as it approaches a traffic light. Make a statement concerning its acceleration.

Explanation

The car is decelerating because it is slowing down. Since the car is traveling in the negative x direction (West), its acceleration is also negative. However, because deceleration is a negative acceleration, the negative sign cancels out and the acceleration is considered positive.

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61. If the velocity versus time graph of an object is a horizontal line, the object is

Explanation

If the velocity versus time graph of an object is a horizontal line, it means that the velocity of the object is not changing over time. This indicates that the object is moving with a constant speed, as there is no acceleration present. The fact that the speed is non-zero means that the object is not at rest, and it is not moving with infinite speed as that would require an infinite slope on the graph.

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62. A boat can move at 30 km/h in still water. How long will it take to move 12 km upstream in a river flowing 6.0 km/h?

Explanation

The boat is moving upstream, which means it is moving against the direction of the river flow. The speed of the boat in still water is 30 km/h, and the speed of the river flow is 6 km/h. To find the time it takes to move 12 km upstream, we can use the formula Time = Distance / Speed. The effective speed of the boat when moving upstream is the difference between its speed in still water and the speed of the river flow, which is 30 km/h - 6 km/h = 24 km/h. Using the formula, we get Time = 12 km / 24 km/h = 0.5 hours, which is equal to 30 minutes. Therefore, it will take 30 minutes for the boat to move 12 km upstream.

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63. An object is moving with constant non-zero acceleration in the +x axis. The velocity versus time graph of this object is

Explanation

The correct answer is a straight line making an angle with the time axis. This is because when an object is moving with constant non-zero acceleration, its velocity increases or decreases at a constant rate. This results in a linear relationship between velocity and time, represented by a straight line. The angle of the line with the time axis represents the rate of change of velocity over time, which is the acceleration.

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64. A bullet shot straight up returns to its starting point in 10 s. What is the initial speed of the bullet?

Explanation

If a bullet shot straight up returns to its starting point in 10 seconds, it means that the total time for the bullet to go up and come back down is 10 seconds. Since the bullet is only affected by gravity during its entire trajectory, the time it takes for the bullet to go up must be half of the total time, which is 5 seconds. Using the equation of motion for vertical motion, we can calculate the initial speed of the bullet. The equation is: final velocity = initial velocity + (acceleration * time). In this case, the final velocity is 0 m/s (since the bullet reaches its highest point and then falls back down), the acceleration is -9.8 m/s^2 (due to gravity), and the time is 5 seconds. Plugging in these values, we can solve for the initial velocity, which comes out to be 49 m/s.

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65. A car decelerates uniformly and comes to a stop after 10 s. The car's average velocity during deceleration was 50 km/h. What was the car's deceleration while slowing down?

Explanation

The car's average velocity during deceleration was given as 50 km/h. The car came to a stop after 10 seconds. Deceleration is the rate at which velocity decreases. The formula for average velocity is total displacement divided by total time. Since the car came to a stop, its total displacement during deceleration is 0. Therefore, the average velocity of 50 km/h is equal to 0 km/h divided by 10 seconds. This simplifies to 0 km/h-s, which is equivalent to 0 km/h-s. Therefore, the car's deceleration while slowing down is 0 km/h-s.

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66. A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Make a statement about the direction of the velocity and acceleration as the ball is coming down.

Explanation

As the ball is coming down, its velocity is directed downward because it is moving in the opposite direction of the initial throw. Additionally, its acceleration is also directed downward because gravity is pulling the ball downward, causing it to accelerate towards the ground. Therefore, both the velocity and acceleration of the ball point downward.

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67. Can an object have increasing speed while its acceleration is decreasing? Support your answer with an example.

Explanation

Yes, an object can have increasing speed while its acceleration is decreasing. An example of this is an object released from rest in the presence of air friction. Initially, the object experiences a high acceleration due to gravity, but as it gains speed, the air friction increases, causing the acceleration to decrease. However, the object's speed continues to increase until it reaches a terminal velocity where the air friction force matches the gravitational force.

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68. An object is moving with constant non-zero acceleration in the +x axis. The position versus time graph of this object is

Explanation

When an object is moving with constant non-zero acceleration in the +x axis, its position versus time graph will be a parabolic curve. This is because the object's velocity is constantly changing due to the acceleration, resulting in a curved trajectory. The steeper the curve, the greater the acceleration. Therefore, a parabolic curve is the correct representation of the position versus time graph for an object with constant non-zero acceleration in the +x axis.

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69. Objects A and B both start from rest. They both accelerate at the same rate. However, object A accelerates for twice the time as object B. What is the distance traveled by object A compared to that of object B?

Explanation

Object A accelerates for twice the time as object B. Since both objects have the same acceleration, the longer duration of acceleration for object A means that it will reach a higher final velocity compared to object B. As a result, object A will cover a greater distance in the same amount of time compared to object B. Therefore, the distance traveled by object A is four times as far as that of object B.

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70. A car traveling 60 km/h accelerates at the rate of 2.0 m/s^2. How much time is required for the car to reach a speed of 90 km/h?

Explanation

The car is initially traveling at a speed of 60 km/h. It then accelerates at a rate of 2.0 m/s^2. To find the time required for the car to reach a speed of 90 km/h, we can convert the speeds to m/s. 60 km/h is equal to 16.67 m/s and 90 km/h is equal to 25 m/s. Using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange the formula to solve for t. Plugging in the values, we get 25 = 16.67 + 2t. Solving for t gives us t = 4.17 seconds, which is approximately equal to 4.2 seconds.

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71. Human reaction time is usually greater than 0.10 s. If your friend holds a ruler between your fingers and releases it without warning, how far can you expect the ruler to fall before you catch it?

Explanation

When your friend releases the ruler without warning, it takes some time for your brain to process the information and send a signal to your fingers to react. This delay is known as human reaction time. Since the question states that human reaction time is usually greater than 0.10 s, it means that it would take at least 0.10 s for you to react and catch the ruler. During this time, the ruler would fall due to gravity. Using the equation d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time, we can calculate the minimum distance the ruler would fall in 0.10 s, which is approximately 4.9 cm. Therefore, you can expect the ruler to fall at least 4.9 cm before you catch it.

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72. If the position versus time graph of an object is a vertical line, the object is

Explanation

If the position versus time graph of an object is a vertical line, it means that the object's position is not changing with time. This indicates that the object is at rest and not moving at all. Therefore, the correct answer is "at rest."

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73. If you run a complete loop around an outdoor track (400 m), in 100 s, your average velocity is

Explanation

If you run a complete loop around an outdoor track in 100 seconds, your average velocity is zero because velocity is defined as the change in position divided by the change in time. Since you end up back at your starting position after running a complete loop, the change in position is zero, resulting in an average velocity of zero.

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74. A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0 s. How high is the building?

Explanation

The height of the building can be determined using the equation of motion for an object in free fall. The equation is h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. In this case, the time is given as 2.0 s. Plugging in the values, we get h = (1/2)(9.8)(2.0)^2 = 19.6 m. Therefore, the height of the building is 19.6 m, which is closest to 20 m among the given options.

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75. Ball A is dropped from the top of a building. One second later, ball B is dropped from the same building. As time progresses, the distance between them

Explanation

As time progresses, the distance between the two balls increases because both balls are subject to the same gravitational force and acceleration. Since ball B is dropped one second after ball A, it starts its descent from a lower height and therefore takes more time to reach the ground. As a result, ball A has a head start and is able to cover more distance in the same amount of time, leading to an increasing distance between the two balls.

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76. A bullet moving horizontally to the right (+x direction) with a speed of 500 m/s strikes a sandbag and penetrates a distance of 10.0 cm. What is the average acceleration, in m/s^2, of the bullet?

Explanation

The average acceleration of the bullet can be calculated using the equation: acceleration = (final velocity - initial velocity) / time. In this case, the bullet is moving horizontally, so its initial and final velocities in the y-direction are both zero. The time it takes for the bullet to penetrate the sandbag can be calculated using the equation: distance = initial velocity * time + 0.5 * acceleration * time^2. Rearranging this equation, we get: time = (2 * distance / acceleration)^0.5. Plugging in the given values for distance (10.0 cm) and initial velocity (500 m/s), we can solve for acceleration. The calculated acceleration is -1.25 * 10^6 m/s^2.

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77. A car starts from rest and accelerates uniformly at 3.0 m/s2. A second car starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s^2. How long does it take the second car to overtake the first car?

Explanation

The first car has a constant acceleration of 3.0 m/s^2. Using the equation of motion, s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the distance traveled by the first car in 6.0 seconds. The distance traveled is given by s = (1/2)(3.0)(6.0)^2 = 54.0 m.

The second car starts from rest and has a constant acceleration of 5.0 m/s^2. Using the same equation of motion, we can calculate the time it takes for the second car to cover a distance of 54.0 m. Rearranging the equation to solve for t, we have t = sqrt(2s/a) = sqrt(2*54.0/5.0) = 6.56 s.

However, the second car starts 6.0 s later, so the total time it takes for the second car to overtake the first car is 6.56 s + 6.0 s = 12.56 s. Rounded to the nearest whole number, the answer is 13 s.

Therefore, the given answer of 21 s is incorrect.

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78. An object starts from rest and undergoes uniform acceleration. During the first second it travels 5.0 m. How far will it travel during the third second?

Explanation

The object undergoes uniform acceleration, which means its velocity increases by the same amount every second. Since it starts from rest, its velocity at the end of the first second will be the same as the acceleration. Therefore, the velocity at the end of the second second will be twice the acceleration, and the velocity at the end of the third second will be three times the acceleration. Since the object travels 5.0 m during the first second, it will travel 5.0 m during the second second and 5.0 m during the third second. Therefore, the total distance traveled during the third second is 5.0 m + 5.0 m = 25 m.

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