Question

the graph shows the momentum y, in newton - seconds, of an object x seconds after the object started moving, for 0 ≤ x ≤ 8. what is the average rate of change, in newton - seconds per second, in the momentum of the object from x = 2 to x = 6?

Explanation:

Step1: Identify the momentum values

From the graph, when \(x = 2\), \(y_1=6\) newton - seconds, and when \(x = 6\), \(y_2 = 9\) newton - seconds.

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

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{\Delta y}{\Delta x}=\frac{f(b)-f(a)}{b - a}\). Here, \(a = 2\), \(b = 6\), \(f(2)=y_1\), and \(f(6)=y_2\). So, \(\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{6 - 2}\).

Step3: Calculate the average rate of change

Substitute \(y_1 = 6\) and \(y_2=9\) into the formula: \(\frac{9 - 6}{6 - 2}=\frac{3}{4}=0.75\) newton - seconds per second.

Answer:

\(0.75\) newton - seconds per second