Question

part 3 of 3
canceling common factors and evaluating the limit, we can finally conclude that the velocity of the ball at ( t = 2 ) is as follows,
\begin{align*} v(2)&=lim_{t
ightarrow2}\frac{(-16t + 18)(t - 2)}{t - 2}\\ &=lim_{t
ightarrow2}-16t + 18\\ &=-16(quad)+18\\ &=quad end{align*}

Explanation:

Step1: Substitute \(t = 2\) into the simplified function

Since the simplified function is \(y=-16t + 18\), when evaluating the limit \(\lim_{t
ightarrow2}(-16t + 18)\), we substitute \(t = 2\) into \(-16t+18\).
So we get \(-16\times(2)+18\).

Step2: Calculate the value

First, calculate \(-16\times2=-32\). Then, \(-32 + 18=-14\).

Answer:

The first blank is \(2\), and the second blank is \(-14\).