Calculate the maximum velocity of the particle in m/s?

Question

A particle moves in a straight line such that the displacement x at any time 't' is given by
x = 6t^2 - t^3 - 3t - 4.
x is in meter and t is in seconds.
Calculate the maximum velocity of the particle in m/s?

Answer 1

dx/dt = velocity = 12t - 3t^2 - 3 = v
dv/dt = 12 - 6t = acceleration
Maximum velocity reached when acceleration = 0
dv/dt = 12 - 6t = 0: t = 2
So max velocity at t = 2: velocity = 12(2) - 3(2^2) - 3 = 24 - 12 - 3
= 9 m/s.