The distance s (In feet) traveled is given by s = 40t-5t^2, where t is the time (in seconds). How far does it travel in coming to a stop?

Question

Have been trying to solve this for hours with no luck, any help would be greatly appreciated. (The question must be solved using Calculus)

Answer 1

s = -5t² + 40t

 

To find the extreme point, take the derivative of s wrt t, set it to zero, and solve for t:

 

ds/dt = -10t + 40

0 = -10t + 40

 

Solve for t.  That is the time it takes to come to a stop.  Plug that value of t into the original equation for s to compute the distance needed to come to a stop. It will only come to an instantaneous stop before reversing direction.