SOLUTION: The velocity v of an object t seconds after it started from the origin is given by 3(v)=3t^2-6t-24. 1. Find the formula for the position. 2. Find the initial velocity. 3. When

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Question 1035439: The velocity v of an object t seconds after it started from the origin is given by 3(v)=3t^2-6t-24.
1. Find the formula for the position.
2. Find the initial velocity.
3. When is the object at rest?
4. When does the object return to the origin.

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
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The velocity v of an object t seconds after it started from the origin is given by 3(v)=3t^2-6t-24. 

0.  Hence, the velocity is v = t%5E2+-+2t+-+8.   (1)


1.  Find the formula for the position.           s(t) = %281%2F3%29%2At%5E3+-+t%5E2+-+8t  (after integration (1) over t).
  
2.  Find the initial velocity.                   -8   ( substitute t = 0 into (1) )

3.  When is the object at rest?                  When t%5E2+-+2t+-8 = 0   (when v(t) = 0.  Find the roots and take the positive root.)

4.  When does the object return to the origin.   When %281%2F3%29%2At%5E3+-+t%5E2+-+8t = 0.   ( Solve it for t using factoring )