The law of motion for the particle is
[tex]S(t) = t^3 -27[/tex]
In order to find the velocity, we have to calculate the derivative of S(t):
[tex]v= S'(t) = \frac{d}{dt} (t^3-27) =3t^2 [/tex]
Similarly, to find the acceleration, we have to calculate the derivative of v(t):
[tex]a(t)= v'(t) = \frac{d}{dt} (3t^2) = 6t [/tex]
