(d) The body is stationary when it has no velocity (when it's not moving).
Velocity is the measure of the rate of change of displacement,
v = s'
s = t^3 + 2t^2 - 4t - 12
Differentiating, applying our power rule to each term,
s' = 3t^2 + 4t - 4
This is our velocity function.
v = 3t^2 + 4t - 4
We want to know when the velocity is zero,
0 = 3t^2 + 4t - 4
Solve for t. You should end up with two values.
A negative t doesn't make sense within the context of the problem.
So disregard that value.
(e) Acceleration is the rate of change of velocity.
So again we take a derivative,
s'' = 6t + 4
This is our acceleration function.
a = 6t + 4
Evaluate this function at t=3.
(f) Remember: The body is stationary when it's velocity = 0. Use your t value that you found in part (d) and plug it into the acceleration function.
