Question

the graph shows the distance a ball has traveled x seconds after it was thrown. what is the average speed between 2 seconds and 8 seconds. distance ball traveled

Explanation:

Step1: Find the change in distance

The distance at \(x = 2\) is \(y_1=3\) meters and at \(x = 8\) is \(y_2 = 6\) meters. The change in distance \(\Delta y=y_2 - y_1\).
\(\Delta y=6 - 3=3\) meters.

Step2: Find the change in time

The time at \(x = 2\) is \(t_1 = 2\) seconds and at \(x = 8\) is \(t_2=8\) seconds. The change in time \(\Delta x=t_2 - t_1\).
\(\Delta x=8 - 2=6\) seconds.

Step3: Calculate the average speed

The formula for average speed (which is the slope of the secant line) is \(v=\frac{\Delta y}{\Delta x}\).
\(v=\frac{3}{6}=\frac{1}{2}=0.5\) meters per second.

Answer:

The average speed between \(2\) seconds and \(8\) seconds is \(0.5\) meters per second.