$1.$ If $\backslash (\backslash$mathrm$\{$s$\}(\backslash$mathrm$\{$t$\})\backslash )$ denotes the position of an object at time $\backslash ($ t $\backslash ),$ then $\backslash ($ s$^\{\backslash$prime$\}($t$)=$v$($t$)\backslash )$ is the instantaneous velocity of the object at time $\backslash ($ t $\backslash ).$ This is one of the fundamental applications of the derivative.

$($a$)$ The graph below in Figure $1$ is a graph of $\backslash ($ s$($t$)\backslash ),$ the position $($in meters$)$ of an object at time $\backslash ($ t $\backslash )($measured in seconds$).$ To the best of your ability, graph $\backslash ($ v$($t$)\backslash ),$ the velocity of the object at time $\backslash ($ t $\backslash )$ in meters per second, on the blank graph in Figure

rigure $1$

$($b$)$ Figure $3$ is the graph of the velocity of a different object at time $\backslash ($ t $\backslash ),$ where the velocity is in meters per second and the time $\backslash ($ t $\backslash )$ is measured in seconds. On the blank graph in Figure $4,$ plot the object's

$\_$nastin. $($in motare$)$ ac a function of $\backslash ($ t $\backslash )($measure