Question

A man runs a 26-mile marathon in 2 hours 14 minutes. The finish line however is only a straight line distance of 18 miles from the starting line. What can you tell about the average velocity and average speed of the runner?A. The average velocity is greater than the average speed.B. The average speed is greater than the average velocity.C. The average speed is positive while the average velocity is negative.D. The average speed is negative while the average velocity is positive.

Answer 1

B. The average speed is greater than the average velocity.

Step-by-step explanation

We want to compare the average speed and average velocity of the man.

To find the average speed, we have to divide the distance the man ran by the time he spent running:

`Speed_{\text{avg}}=(Dis\tan ce)/(Time)`

He ran 26 miles in 2 hours 14 mins (2.233 hrs). Therefore, his average speed is:

`\begin{gathered} Speed_{\text{avg}}=(26)/(2.233) \\ Speed_(avg)=11.64\text{ mi/hr} \end{gathered}`

To find the average velocity, we have to divide the man's displacement (how far he is from his starting point) by the time he spent running:

`Velocity_{\text{avg}}=(Displacement)/(Time)`

His displacement from his starting point is 18 miles. Therefore, his average velocity is:

`\begin{gathered} Velocity_{\text{avg}}=(18)/(2.233) \\ Velocity_{\text{avg}}=8.06\text{ mi/hr} \end{gathered}`

Therefore, as we can see, the average speed is greater than the average velocity.