Question

Displacement, velocity and acceleration problems- questions d,e, and f

Answer 1

(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.