A car is traveling on a straight road. For seconds, the cars velocity , in meters per second, is modeled by the piecewise-linear function defined by the graph below.

a.) Find . Using correct units, explain the meaning of .

b.) For each of and , find the value or explain why it does not exist. Indicate units of measure.

c.) Let be the cars acceleration at time , in meters per second per second. For , write a piecewise-defined function for .

d.) Find the average rate of change of over the interval . Does the mean value theorem guarentee a value of c, for , such that is equal to the average rate of change. Why or why not?

For a.) I came up with the answer 360 meters, I'm pretty sure that is correct.

For b.), I think the acceleration would be zero, correct me if I'm wrong.

I don't know what to do for c.) and d.) any help is appreciated, thanks.