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?

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