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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.

 Jun 22, 2018
 #1
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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)

 

 

 

cool cool cool

 Jun 23, 2018

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