Let

h $=$ s$($t$)=43$t $16$t$2$

give the height of the ball at time t$.$

Then the ball's velocity at time

t $=$ a

can be found by

v$($a$)=$lim$$t$$a$$

s$($t$)$ s$($a$)$t $$ a

$.$

We are asked to find the velocity at

t $=2$;

therefore we use

a $=$

and have

v$(2)=$lim$$t$2$

s$($t$)$ s$(2)$t $2$

$=$lim$$t$2$

$43$t $16$t$2$

$$

$43$

$16(2)2$

t $2$

$=$lim$$t$2$

$43$t $16$t$2$

$$ t $2$

$.$