1) The velocity of the particle is given by the derivative of the position. So, if we derive s(t), we get the velocity of the particle as a function of the time:
[tex] v(t)=s'(t)=(2t^3-3t^2-36t+6)'=6t^2-6t-36 [/tex]
2) The acceleration of the particle is given by the derivative of the velocity. So, if we derive v(t), we get the acceleration of the particle as a function of the time:
[tex] a(t)=v'(t)=(6t^2-6t-36)'=12t-6 [/tex]
