Answer
$v(2) =-24 $ft/s
Work Step by Step
Given the function $s(t) = 40t - 16t^2$
You can get the velocity by evaluating the derivative at $t = 2$
$ v(2) = \lim\limits_{t \to 2}\frac{s(t) - s(2)}{t-2}$
Substitute $s(t)$ and $s(2) (= 80 - 64 = 16)$
$ v(2) = \lim\limits_{t \to 2}\frac{(40t - 16t^2) - 16}{t-2}$
Factor the top
$ v(2) = \lim\limits_{t \to 2}\frac{-8(2t^2-5t+2)}{t-2}$
$ v(2) = \lim\limits_{t \to 2}\frac{-8(t-2)(2t-1)}{t-2}$
Simplify the expression ($(t-2)$ cancels)
$ v(2) = \lim\limits_{t \to 2}-8(2t-1)$
$ v(2) =-8 \lim\limits_{t \to 2}(2t-1)$
Find the limit
$ v(2) =-8 \lim\limits_{t \to 2}(2(2)-1)$
$ v(2) =-8 \lim\limits_{t \to 2}(3)$
$ v(2) =-8 (3)$
$ v(2) =-24$
The instantaneous velocity at 2 seconds is $-24$ft/s
