A particle moves in a straight line with displacement function s(t) = 12t 2t 3 1

QUESTION:

A particle moves in a straight line with displacement function s(t) = 12t 2t 3 1 centimetres where t is in seconds, t > 0. a Find velocity and acceleration functions for the particles motion. b Find the initial conditions and interpret their meaning. c Find the times and positions when the particle reverses direction. d At what times is the particles: i speed increasing ii velocity increasing?