Question 1035439
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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.


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0.  Hence, the velocity is v = {{{t^2 - 2t - 8}}}.   (1)


1.  Find the formula for the position.           s(t) = {{{(1/3)*t^3 - t^2 - 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^2 - 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 {{{(1/3)*t^3 - t^2 - 8t}}} = {{{0}}}.   ( Solve it for t using factoring )
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