4. Applications of Derivatives

Given the position equation $s\(\left\)(t\(\right\))$, calculate the average velocity (in meters per second) based on the given interval, and the instantaneous velocity (in meters per second) at the end of the time interval.

$s\(\left\)(t\(\right\))=9t-t^2$, $0\(\le\) t\(\le\)3$

Given the position equation $s\(\left\)(t\(\right\))$ , calculate the average velocity (in meters per second) based on the given time interval, and the instantaneous velocity (in meters per second) at the end of the time interval.

$s\(\left\)(t\(\right\))=\(\frac{30}{t+5}\)$, $-4\(\le\) t\(\le\)0$

Given the position of an object $s\(\left\)(t\(\right\))=12t-t^2$ (in meters), find the acceleration of the object at $t=5$ seconds.

Given below is the graph of velocity with respect to time. At which time(s) would acceleration be 0?