Chapter 5.7, Problem 31ES

Suppose that at time $t=0$ a particle is at the origin of an $x\text{-axis}$ and has a velocity of ${\upsilon }_0=25\text{ cm/s}$ . For the first $4\text{ s}$ thereafter it has no acceleration, and then it is acted on by a retarding force that produces a constant negative acceleration of $a=-10{\text{ cm/s}}^2$ .

(a) Sketch the acceleration versus time curve over the interval $0\le t\le 12$ .

(b) Sketch the velocity versus time curve over the time interval $0\le t\le 12$ .

(c) Find the $x\text{-}$ coordinate of the particle at times $t=8\text{ s}$ and $t=12\text{ s}$ .

(d) What is the maximum $x\text{-}$ coordinate of the particle over the time interval $0\le t\le 12$ ?