Question 1147472
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(a) The velocity is the first derivative of the position function over time

        v(t) = {{{(ds)/(dt)}}} = 3t^2 - 22t + 24.     (1)

     To find v(5),  substitute t= 5 into the formula (1)

     

    The acceleration is the second derivative of the position function over time

        a(t) = {{{(d^2s)/(dt^2)}}} = 6t - 22.       (2)

     To find a(5),  substitute t= 5 into the formula (2).



(b)  At t= 5,  v(5) = -11,   a(5) = 8.


     So, the particle moves in negative direction and has positive acceleration.


     In the normal human language, it means that the particle DECELERATES (slowing down, moving in negative direction).
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