Question

The position of a certain particle is given by the function s(t)=t⁴−4t³+2 where s is measured in meters and t is measured in seconds. First find the times at which the acceleration is 0 , then find its position and velocity at these times.

Answer 1

Explanation:

velocity is the first derivative of the given position function:

velocity = 4 t^3 - 12t^2

acceleration is the second derivative of the position function

accel = 12 t^2 - 24 t

this = 0 at t= 0 and 2 seconds

Using these values in the velocity function shows v = 0 and 0 m/s

Using these values in the position equation shows s = 2 and - 14 m