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.
+128407 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)
