can someone explain what s is in the following limit?

Question

anonymous · Answer

attachment

anonymous · Answer

height of said brush at t seconds

auctoratrox · Answer

The "s(t)" stands for a position function. Does this help?

anonymous · Answer

at $t=2,s(t)=-16\times 2^2+100=36$ and so  you want 
$$\frac{36-(-16t^2+100)}{2-t}$$

anonymous · Answer

we get 
$$\frac{36+16t^2-100}{2-t}=\frac{16t^2-64}{2-t}$$
$$=\frac{16(t^2-4)}{2-t}=\frac{16(t+2)(t-2)}{2-t}$$
$$=-16(t+2)$$ 
replace $t$ by 2 to get your answer

anonymous · Answer

oh i get the s part, but if i put 2 in for t, that would give me zero...

anonymous · Answer

you get $\frac{0}{0}$ until you factor and cancel

anonymous · Answer

okay got it! thanks! :)

anonymous · Answer

once you factor and cancel you can replace $t$ by 2

anonymous · Answer

btw it always works this way, although in one week you will be taught a snap method and will be able to do this in your head on 3 seconds, and then get annoyed that you had to do it this way

anonymous · Answer

you will say "the derivative of $-16t^2+100$ is $-32t$ replace $t$ by $2$ get $-64$

anonymous · Answer

haha i think derivatives are for calc, im only in precal