Chapter 9, Problem 19P

Determine the velocity $v\left(t\right)$ and the position $y\left(t\right)$ of a vehicle that starts from rest at position $y\left(0\right)=0$ and is subjected to the following accelerations:

(a) $a\left(t\right)=40t^3+30t^{\text{2}}+20t+10{\text{m/s}}^{\text{2}}$ (b) $a\left(t\right)=4\sin 2t\cos 2t{\text{m/s}}^{\text{2}}$ Hint: Use a trigonometric identity.