Problem 1.97

At the moment $t=0$ a stationary particle of mass $m$ experiences a time-dependent force $\mathbf{F}=\mathbf{a} t(\tau-t),$ where a is a constant vector, $\tau$ is the time during which the given force acts. Find: (a) the momentum of the particle when the action of the force discontinued: (b) the distance covered by the particle while the force acted.