Acceleration, Distance And Time Reasoning Test! Trivia Quiz

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.

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.

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.

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.

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.

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.