Question

A man runs a 26-mile marathon in 2 h 14 min. 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?

Answer 1

The average speed is greater than the magnitude average velocity because the total distance is greater than the displacement of the man.

Step-by-step explanation:

First, let's write 2h 14 min as a decimal, so:

`\begin{gathered} 14\min *\frac{1\text{ hour}}{60\text{ min}}=0.23\text{ hours} \\ 2\text{ h 14 min = 2.23 hours} \end{gathered}`

Now, the average velocity is equal to the division of the displacement by time. The displacement is the straight-line distance, so the average velocity is:

`\text{Average velocity = }\frac{18\text{ miles}}{2.23\text{ hours}}=8.07\text{ miles per hour}`

On the other hand, the average speed is the division of the total distance by time, so the average speed is:

`\text{Average speed = }\frac{26\text{ miles}}{2.23\text{ hours}}=11.66\text{ miles per hour}`

Therefore, the average speed is greater than the magnitude average velocity because the total distance is greater than the displacement of the man.