An object is moving along a straight line. Its position (in meters) from the starting point at time t (measured in seconds) is described by s(t)=t^3-3t. Answer the following.

Find the position of the object at the time moment when its instantaneous velocity is zero for the first time.

Guest Jun 22, 2018

#1**+2 **

s(t) = t^3 - 3t

The velocity is given by the derivative of this function =

s ' (t) = 3t^2 - 3

Setting the velocity to 0 and solving for t, we have

3t^2 - 3 = 0 factor

3 (t^2 - 1) = 0 divide through by 3

t^2 - 1 =0

(t + 1) ( t - 1) = 0

Setting both factors to 0 and solving for t, we have that

t = - 1 seconds or t = 1 second

Assuming that the time is ≥ 0....its velocity is 0 at 1 second and its position is

(1)^3 - 3(1) = -2 ⇒ (2 meters to the left of its starting position)

CPhill
Jun 23, 2018