2. A car is traveling on a straight road. For 0≤1≤24 seconds, the car's velocity (1), in meters per second, is modeled by the piecewise-linear function defined by the graph below. v(1) Velocity (meters per second) 0 20 15- 10+ (4,20) (16, 20) 8 12 16 20 24 Time (seconds) a) Find v(1)dt. Using correct units, explain the meaning of v(1)dt. b) For each of v'(4) and v'(20), find the value or explain why it does not exist. Indicate units of measure. c) Let a(t) be the car's acceleration at time t, in meters per second per second. For 0 <1 < 24, write a piecewise-defined function for a(1). d) Find the average rate of change of v over the interval 8≤1≤20. Does the Mean Value Theorem guarantee a value of c, 8<c<20, such that v'(c) is equal to this average rate of change? Why or why not?

Fig: 1