Chapter 6.1, Problem 27E

Piecewise velocity The velocity of a (fast) automobile on a straight highway is given by the function

$v(t)=\{\begin{array}{ll}3t\hfill & \text{if}0\le t<20\hfill \\ 60\hfill & \text{if}20\le t<45\hfill \\ 240\hfill & \text{if}t\ge 45,\hfill \end{array}$

where t is measured in seconds and v has units of m/s.

1. a. Graph the velocity function, for 0 ≤ t ≤ 70. When is the velocity a maximum? When is the velocity zero?
2. b. What is the distance traveled by the automobile in the first 30 s?
3. c. What is the distance traveled by the automobile in the first 60 s?
4. d. What is the position of the automobile when t = 75?