Physics

Problem

A car moves in a straight line. Its acceleration, in meters per second squared, is piecewise constant as summarized in the table.

Time interval (s)	$[0,4]$	$(4,7]$	$(7,10]$
Acceleration $a(t)$ (m/s $^2$ )	$2$	$-3$	$0$

t=0

, the car’s velocity is

5\text{ m/s}

and its position is

0\text{ m}

. a. Derive an explicit piecewise expression for the velocity function

v(t)

for

0\le t\le 10

. b. Determine the exact time, if any, at which the car reverses direction on the interval

0\le t\le 10

seconds. Justify your conclusion. c. Compute the car’s position at

t=10

seconds. d. Find the total distance traveled by the car during the first

10

seconds.