Acceleration, Distance And Time Reasoning Test! Trivia Quiz

1. If a car accelerates uniformly from 0 to 60 km/h in 10 seconds, what is its acceleration?

6 m/s²

1.67 m/s²

10 m/s²

3.33 m/s²

To find the acceleration, use the formula:

Acceleration (a) = (Final Velocity - Initial Velocity) / Time

Given that the initial velocity is 0 km/h (converted to 0 m/s), the final velocity is 60 km/h (converted to 16.67 m/s), and the time is 10 seconds:

a = (16.67 m/s - 0 m/s) / 10 s = 1.67 m/s²

Therefore, the correct answer is 1.67 m/s².

Explanation

To find the acceleration, use the formula:

Acceleration (a) = (Final Velocity - Initial Velocity) / Time

Given that the initial velocity is 0 km/h (converted to 0 m/s), the final velocity is 60 km/h (converted to 16.67 m/s), and the time is 10 seconds:

a = (16.67 m/s - 0 m/s) / 10 s = 1.67 m/s²

Therefore, the correct answer is 1.67 m/s².

2. A train travels at a constant speed of 90 km/h. How far does it travel in 2 hours?

45 km

90 km

180 km

150 km

To calculate the distance traveled, use the formula:

Distance = Speed x Time

Given that the speed is 90 km/h and the time is 2 hours:

Distance = 90 km/h x 2 h = 180 km

Therefore, the correct answer is 180 km.

Explanation

To calculate the distance traveled, use the formula:

Distance = Speed x Time

Given that the speed is 90 km/h and the time is 2 hours:

Distance = 90 km/h x 2 h = 180 km

Therefore, the correct answer is 180 km.

3. What distance will an object cover in 5 seconds if it is moving with a uniform acceleration of 2 m/s² from rest?

10 m

15 m

25 m

5 m

To find the distance covered under uniform acceleration from rest, use the formula:

Distance (s) = 0.5 x a x t²

Given that the acceleration (a) is 2 m/s² and the time (t) is 5 seconds:

s = 0.5 x 2 m/s² x (5 s)² = 0.5 x 2 x 25 = 25 m

Therefore, the correct answer is 25 m.

Explanation

To find the distance covered under uniform acceleration from rest, use the formula:

Distance (s) = 0.5 x a x t²

Given that the acceleration (a) is 2 m/s² and the time (t) is 5 seconds:

s = 0.5 x 2 m/s² x (5 s)² = 0.5 x 2 x 25 = 25 m

Therefore, the correct answer is 25 m.

4. An object moves with a constant velocity of 5 m/s for 8 seconds. What is the total distance covered?

30 m

35 m

40 m

50 m

To calculate the distance covered at constant velocity, use the formula:

Distance = Velocity x Time

Given that the velocity is 5 m/s and the time is 8 seconds:

Distance = 5 m/s x 8 s = 40 m

Therefore, the correct answer is 40 m.

Explanation

To calculate the distance covered at constant velocity, use the formula:

Distance = Velocity x Time

Given that the velocity is 5 m/s and the time is 8 seconds:

Distance = 5 m/s x 8 s = 40 m

Therefore, the correct answer is 40 m.

5. A bullet comes to rest in a block of wood in 1.0 x 10^-2 seconds, with an acceleration of -8.0 x 10^4 metres per second squared. What was its original speed, in metres per second?

-800 m/s

800 m/s

12.5 m/s

-12.5 m/s

The bullet comes to rest in the block of wood, which means its final velocity is 0 m/s. The acceleration is given as -8.0 x 10^4 m/s^2, indicating that the bullet is decelerating. 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 substitute the given values. Since v = 0 m/s, a = -8.0 x 10^4 m/s^2, and t = 1.0 x 10^-2 s, we can solve for u. Rearranging the equation, we have u = v - at. Plugging in the values, we get u = 0 m/s - (-8.0 x 10^4 m/s^2)(1.0 x 10^-2 s) = 800 m/s. Therefore, the original speed of the bullet was 800 m/s.

Explanation

The bullet comes to rest in the block of wood, which means its final velocity is 0 m/s. The acceleration is given as -8.0 x 10^4 m/s^2, indicating that the bullet is decelerating. 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 substitute the given values. Since v = 0 m/s, a = -8.0 x 10^4 m/s^2, and t = 1.0 x 10^-2 s, we can solve for u. Rearranging the equation, we have u = v - at. Plugging in the values, we get u = 0 m/s - (-8.0 x 10^4 m/s^2)(1.0 x 10^-2 s) = 800 m/s. Therefore, the original speed of the bullet was 800 m/s.

6. The light turns red, and you come to a screeching halt. Checking your stopwatch, you see that you stopped in 4.5 seconds. Your deceleration was 1.23 x 10^-3 miles per second squared. What was your original speed in miles per hour?

21.6 miles/hour

0.006 miles/hour

0.36 miles/hour

0.0001 miles/hour

To find the original speed, we need to use the formula: final velocity = initial velocity + acceleration * time. In this case, the final velocity is 0 since the car comes to a stop. The acceleration is given as 1.23 x 10^-3 miles per second squared and the time is 4.5 seconds. Plugging these values into the formula, we get: 0 = initial velocity + (1.23 x 10^-3) * 4.5. Solving for the initial velocity, we find that it is 21.6 miles per hour.

Explanation

To find the original speed, we need to use the formula: final velocity = initial velocity + acceleration * time. In this case, the final velocity is 0 since the car comes to a stop. The acceleration is given as 1.23 x 10^-3 miles per second squared and the time is 4.5 seconds. Plugging these values into the formula, we get: 0 = initial velocity + (1.23 x 10^-3) * 4.5. Solving for the initial velocity, we find that it is 21.6 miles per hour.

7. A motorcycle is going 60 miles per hour and decelerating at 60 miles per hour squared. How far does it go in 1 hour?

90 miles

60 miles

30 miles

120 miles

The motorcycle is decelerating at a rate of 60 miles per hour squared, which means its speed is decreasing by 60 miles per hour every hour. Therefore, after 1 hour, the motorcycle's speed would be reduced to 0 miles per hour. Since the motorcycle was initially traveling at 60 miles per hour, it would have covered a distance of 60 miles in that 1 hour.

Explanation

The motorcycle is decelerating at a rate of 60 miles per hour squared, which means its speed is decreasing by 60 miles per hour every hour. Therefore, after 1 hour, the motorcycle's speed would be reduced to 0 miles per hour. Since the motorcycle was initially traveling at 60 miles per hour, it would have covered a distance of 60 miles in that 1 hour.

8. A block of wood is shooting down a track at 10 metres per second and is slowing down because of friction. If it comes to rest in 20 seconds and 100 metres, what is its deceleration, in metres per second squared?

-0.5 m/s^2

0.5 m/s^2

1.5 m/s^2

-1.5 m/s^2

The block of wood is slowing down due to friction, which means it is experiencing deceleration. The question asks for the deceleration in meters per second squared. To find this, we can use the equation of motion: final velocity squared equals initial velocity squared plus 2 times acceleration times distance. Since the final velocity is 0 (since it comes to rest), the initial velocity is 10 m/s, and the distance is 100 meters, we can rearrange the equation to solve for acceleration. Plugging in the values, we get -0.5 m/s^2 as the deceleration.

Explanation

The block of wood is slowing down due to friction, which means it is experiencing deceleration. The question asks for the deceleration in meters per second squared. To find this, we can use the equation of motion: final velocity squared equals initial velocity squared plus 2 times acceleration times distance. Since the final velocity is 0 (since it comes to rest), the initial velocity is 10 m/s, and the distance is 100 meters, we can rearrange the equation to solve for acceleration. Plugging in the values, we get -0.5 m/s^2 as the deceleration.

9. A car is going 60 miles per hour and accelerating at 10 miles per hour squared. How far does it go in 1 hour?

70 miles

35 miles

65 miles

30 miles

Since the car is traveling at a constant speed of 60 miles per hour and accelerating at a rate of 10 miles per hour squared, it means that the car is not changing its speed. Therefore, the distance it travels in 1 hour would be the same as its speed, which is 60 miles per hour. Hence, the correct answer is 65 miles.

Explanation

Since the car is traveling at a constant speed of 60 miles per hour and accelerating at a rate of 10 miles per hour squared, it means that the car is not changing its speed. Therefore, the distance it travels in 1 hour would be the same as its speed, which is 60 miles per hour. Hence, the correct answer is 65 miles.

10. A car starts from rest and is accelerated at 5.0 metres per second squared. What is its speed 500 metres later?

26 m/s

50 m/s

5000 m/s

70.7 m/s

The car is accelerating at a constant rate of 5.0 m/s^2. Using the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 since the car starts from rest), a is the acceleration, and t is the time, we can calculate the time it takes for the car to reach a speed of 70.7 m/s. Rearranging the equation to solve for t, we have t = (v - u) / a. Plugging in the values, t = (70.7 - 0) / 5.0 = 14.14 seconds. Now, using the equation s = ut + 0.5at^2, where s is the displacement, we can calculate the distance traveled by the car in 14.14 seconds. Rearranging the equation to solve for s, we have s = ut + 0.5at^2 = 0 + 0.5 * 5.0 * (14.14)^2 = 500 meters. Therefore, the speed of the car 500 meters later is 70.7 m/s.

Explanation

The car is accelerating at a constant rate of 5.0 m/s^2. Using the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 since the car starts from rest), a is the acceleration, and t is the time, we can calculate the time it takes for the car to reach a speed of 70.7 m/s. Rearranging the equation to solve for t, we have t = (v - u) / a. Plugging in the values, t = (70.7 - 0) / 5.0 = 14.14 seconds. Now, using the equation s = ut + 0.5at^2, where s is the displacement, we can calculate the distance traveled by the car in 14.14 seconds. Rearranging the equation to solve for s, we have s = ut + 0.5at^2 = 0 + 0.5 * 5.0 * (14.14)^2 = 500 meters. Therefore, the speed of the car 500 meters later is 70.7 m/s.