$(3)$ What is the average velocity at a specific time $t=t_0$ and $t=t_1$ of a particle in motion where its position $(y)$ is a real valued function of time $(t)$; that is$,y=y(t)?$ What is the instantaneous velocity at $t=t_0?$ Explain with the example $y=t^2+2t$ for $t_0=1$ second and $t_1=2,1\mathrm{.}5,1\mathrm{.}1,1\mathrm{.}01$ seconds.

$(4)$ If a ball is thrown into the air with a velocity of $60f\frac{t}{sec},$ its height in feet is given by $y=60t-16t^2$ where $t$ denotes time in seconds.

$($a$)$ Find the average velocity for the time period beginning when $t=3$ seconds and lasting $0\mathrm{.}5,0\mathrm{.}1,0\mathrm{.}05,$ and $0\mathrm{.}01$ seconds.

$($b$)$ Estimate the instantaneous velocity when $t=3$ seconds.