3.6 Exercise 38

The position of a particle moving along the x-axis varies with time according to $x \left(t\right) = 5.0 t^{2} - 4.0 t^{3}$ m. Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t = 2.0 s, (c) the time at which the position is a maximum, (d) the time at which the velocity is zero, and (e) the maximum position.