# Applications of Integrals

1. Oct 21, 2008

1. The problem statement, all variables and given/known data

In coming to a stop the acceleration of a car is given as a= -4t. If it is traveling at 32m/s when the brakes are applied, how far does is travel while stopping?

3. The attempt at a solution

1.) Integrate acceleration to find velocity as a function of time

v= -2t^2 + C1

at t=0 , v = 32m/s

v = -2t^2 + 32

2.) Integrate velocity to find displacement as a funtion of time

s = (2/3)(t^3) + 32t + C2.

This is where I get stuck.

Is it correct to assume that at t=0 , s will be zero and therefore C2 is zero?

2. Oct 22, 2008

### HallsofIvy

Staff Emeritus
It's your coordinate system so it's your choice! The problem asks for the distance the car travels- that is the difference between s when the car stops and s when the car is going 32 m/s. Yes you can take "s= 0" to be the point at which the car is going 32 m/s. In fact, if you take s to be any number you like, when you do the subtraction, that number will cancel.