Answer
$$v=-39.2$$
Work Step by Step
We can find the velocity of the object at $t=4$ by substituting $a=4$ into the definition of velocity given in the question as follows.$$v(a=4)=\lim_{t \to 4}\frac{s(4)-s(t)}{4-t}=\lim_{t \to 4}\frac{(-4.9(4^2)+250)-(-4.9t^2+250)}{4-t}=\lim_{t \to 4}\frac{4.9(t^2-4^2)}{4-t}=\lim_{x \to 4} - \frac{4.9(t+4)(t-4)}{t-4}=\lim_{x \to 4}-4.9(t+4)=-39.2$$
