After brakes are applied how far does the car travel? - integrating twice

[calculusisfun]

Homework Statement

t seconds after the brakes of a car are put on, the acceleration of the car is a(t) = -6t - 4 ft/sec^2. If the automobile was moving at the speed of 32 ft/sec when the brakes were put on, how far does it go before stopping?

Homework Equations

a(t) = -6t - 4 ft/sec^2

The Attempt at a Solution

integral of a(t) = -6t - 4 ft/sec^2 ----> |-3t^2 - 4t + c| = 32
I put the absolute value because it is the speed. is that right?

v(0) = c = 32

v(t) = -3t^2 -4t + 32

-3t^2 -4t + 32 = 0
t = 8/3

integral from 0 to 8/3 of -3t^2 -4t + 32

= 52.1481 ft

The main thing I am worried about is that it says speed instead of velocity, can anyone help me out here? Thanks! :)

 

[rock.freak667]

That should be correct what you did.

But you don't need the modulus sign really.