calculus question

Question

A cyclist traveling at 40ft/s decelerates at a constant 4ft/s^2. How many feet does she travel before aiming to a complete stop?

Answer 1

acceleration a = r" = -4

Integrate to get the velocity. r' = -4t +C

Find the value of C by noting that at t = 0, r' = 40           C =40

r' = -4t + 40

The cyclist comes to a stop when its velocity r' = 0        -4t + 40 = 0        t = 10

To find the distance traveled by the cyclist between t = 0 and t = 10,

integrate the velocity function to get

r = - 2 t ² + 40 t    = 200 m