[ConsoleMaster]

A motorbike is moving at 21.3 m/s when the rider applies the brakes, causing the motorbike to slow down at a constant rate. During the 3.00-s interval immediately after braking begins, the speed decreases to half its starting value. What distance does the motorbike travel from the instant braking begins until it comes to rest?

[CommDweeb]

First determine the rate of deceleration.

If the speed decreases by 1/2 from 21.3 mertes/second in 3 seconds, the rate of deceleration is 3.55 mertes/second. This can be verified by multiplying acceleration by 6 seconds, and this does indeed yield 21.3.

D = t^2 * a / 2, where d is distance, t is time, and a is acceleration.

To get the distance traveled while decelerating, you subtract the distance it takes to accelerate to 10.65 meters/second (d1) from the distance it takes to accelerate to 21.3 meters/second (d2)

D1 = 9 * 3.55/2 = 15.975 meters
D2 = 36 * 3.55/2 = 63.9 meters

The answer is d2 - d1 = 47.925 meters ;D