A car is traveling on a straight road with velocity $55\,\mathrm{ft/sec}$ at time $t = 0$. For $0 \leq t \leq 18$ seconds, the car's acceleration $a(t)$, in $\mathrm{ft/sec}^{2}$, is the piecewise linear function defined by the graph above. (a) Is the velocity of the car increasing at $t = 2$ seconds? Why or why not? (b) At what time in the interval $0 \leq t \leq 18$, other than $t = 0$, is the velocity of the car $55\,\mathrm{ft/sec}$? Why? (c) On the time interval $0 \leq t \leq 18$, what is the car's absolute maximum velocity, in $\mathrm{ft/sec}$, and at what time does it occur? Justify your answer. (d) At what times in the interval $0 \leq t \leq 18$, if any, is the car's velocity equal to zero? Justify your answer.
A car is traveling on a straight road with velocity $55\,\mathrm{ft/sec}$ at time $t = 0$. For $0 \leq t \leq 18$ seconds, the car's acceleration $a(t)$, in $\mathrm{ft/sec}^{2}$, is the piecewise linear function defined by the graph above.\\
(a) Is the velocity of the car increasing at $t = 2$ seconds? Why or why not?\\
(b) At what time in the interval $0 \leq t \leq 18$, other than $t = 0$, is the velocity of the car $55\,\mathrm{ft/sec}$? Why?\\
(c) On the time interval $0 \leq t \leq 18$, what is the car's absolute maximum velocity, in $\mathrm{ft/sec}$, and at what time does it occur? Justify your answer.\\
(d) At what times in the interval $0 \leq t \leq 18$, if any, is the car's velocity equal to zero? Justify your answer.