Originally Posted by
topsquark To put it in a single statement, what you are looking for is:
$\displaystyle s=\int_{-1}^6 dt \, |v(t)|$
In other words, we need to find out if and where the object turns around.
$\displaystyle v(t)=3t^2-12t$
The velocity has zeros at t = 0 s and t= 4 s. Since v(t) is positive at t = -1, the object starts moving from position -2 and moves in the +x direction to t = 0 s at position 5 (7 units total distance) and turns around. It goes in the -x direction to t = 4 s at position -27 (34 units total distance) and turns around. It goes in the +x direction to t = 6 s at position 5 (66 units total distance.) So the object moves a total of 66 units.
-Dan