Chapter 16.2, Problem 70E

(a)

To determine

To calculate: The speed of the top of the moving car and the direction of its motion at times $t=0$ and $t=0.25$ if a worn shock absorber on a car experiences damped harmonic motion at $t=0$ such that the height of the car frame after t seconds is given by the equation $p\left(t\right)=4.2e^{-0.5t}\sin \left(2\pi t+\frac{\pi }{2}\right)$ centimeters above the rest position.

(b)

To determine

To graph: The functions $p$ and $p^{\prime }$ for t for $0\le t\le 10$ and also for $0\le t\le 2$ and then estimate to the nearest hundredth of a second the time at which the velocity of the car is greatest in upward direction using graphs and graphing technology.