Chapter 9, Problem 20P

A particle starts from rest at a position $x\left(0\right)=0$. Find the velocity $v\left(t\right)$ and position $x\left(t\right)$ if the particle is subjected to the following accelerations:

(a) $a\left(t\right)=6t^3-4t^{\text{2}}+7t-8{\text{m/s}}^{\text{2}}$ (b) $a\left(t\right)=5e^{-5t}+\frac{\pi }{4}\cos \left(\frac{\pi }{4}t\right){\text{m/s}}^{\text{2}}$