Question

The position of a particle moving along the x axis is given by  , where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?

Answer 1

Assume the position of the particle is

$$x=4t^2-t^3.$$

Being the first derivative of position by time, velocity is

$$v=8t-t^2.$$

Therefore, the maximum velocity in positive x direction is when

$$t=8\text{ s}.$$

The position is x=-256.