The velocity of a particle moving along a line is given by $v(t) = t^3 - 4 t^2$ meters per second. Find the displacement of the particle during the time interval between -2 and 5 seconds.

Displacement = (Include the correct units.)

To find the total distance traveled by the particle during the time interval from -2 to 5 seconds, we must split the integral of the absolute value of velocity into a sum of two integrals

Total distance traveled = $\displaystyle \int_{-2}^{5} | t^3 - 4 t^2 | \, dt = \int_{-2}^{k} v_1(t) \, dt + \int_{k}^{5} v_2(t) \, dt$

where $v_1(t)$ and $v_2(t)$ are functions and $k$ is a number such that

$v_1(t) =$ (Absolute values are not allowed.)
$v_2(t) =$ (Absolute values are not allowed.)
$k =$

Total distance traveled = (Include the correct units.)

Hint: