An object moving along a horizontal axis has its instantaneous velocity at time $t$ in seconds given by the function $v$ pictured in Figure $4\mathrm{.}1\mathrm{.}12,$ where $v$ is measured in feet $\frac{?}{sec}.$ Assume that the curves that make up the parts of the graph of $y=v(t)$ are either portions of straight lines or portions of circles.

Figure $4\mathrm{.}1\mathrm{.}12.$ The graph of $y=v(t),$ the velocity function of a moving object.

a$.$ Determine the exact total distance the object traveled on $0t2.$

b$.$ What is the value and meaning of $s(5)-s(2),$ where $y=s(t)$ is the position function of the moving object?

c$.$ On which time interval did the object travel the greatest distance: $0,2.2,4,$ or $5,7?$

d$.$ On which time interval$($s$)$ is the position function $s$ increasing? At which point$($s$)$ does $s$ achieve a relative maximum?

ANSWER EVERY OPTION IF POSSIBLE IF NOT ONLY C$.$ FOLLOW THIS FORMAT: $1.$ Specific sentence: conclusion. Use course terminology and underline the terminology

$2.$ Second sentence: facts. Use course terminology and underline terminology

$3.$ Third sentence: reasoning. Use course terminology and underline it