Question

workspace: the graph represents the velocity of souvenirs shot from an air cannon into the crowd during a football game. when shot, the souvenir has an initial velocity of 260 feet per second (fps). what is the average rate of change in velocity over the interval from 1 - 3 seconds? show your work below

Explanation:

Step1: Identify the velocity at endpoints

From the graph, at $t = 1$ second, the velocity $v_1=150$ fps, and at $t = 3$ seconds, the velocity $v_2 = 50$ fps.

Step2: Use the average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, the function is velocity $v(t)$, $a = 1$, $b = 3$, so the average rate of change of velocity $\frac{\Delta v}{\Delta t}=\frac{v_2 - v_1}{3 - 1}$.
Substitute $v_1 = 150$ and $v_2 = 50$ into the formula: $\frac{50-150}{3 - 1}=\frac{- 100}{2}=-50$ fps per second.

Answer:

$-50$ feet per second per second