Chapter 2, Problem 9P

(a)

To determine

The average speed of the person

Answer to Problem 9P

The average speed of the person is $\text{4}\text{.3 m/s}$ .

Explanation of Solution

Given:

The number of complete laps

  $n=8$

Distance of one lap, $l=0.25\text{ mi}$

Total time taken, $t=12.5\text{ min}$

Formula used:

The average speed of the person is given by,

  $\overline{v}=\frac{d}{t}$    ……(1)

Here, $d$ is the total distance travelled in the time $t$ , which is given by,

  $d=n\times l$    ……(2)

Calculation:

Convert the distance of one lap into meters.

  $\begin{array}{c}l=\left(0.25\text{ mi}\right)\left(\frac{1610\text{ m}}{1\text{ mi}}\right)\\ =402.5\text{ m}\end{array}$

The total distance travelled using equation (2) is,

  $\begin{array}{c}d=n\times l\\ =8\left(402.5\text{ m}\right)\\ =3220\text{ m}\end{array}$

Express the time taken in seconds.

  $\begin{array}{c}t=\left(12.5\text{ min}\right)\left(\frac{60\text{ s}}{1\text{ min}}\right)\\ =750\text{ s}\end{array}$

Substitute the calculated values of $d$ and $t$ in equation (1) and determine the value of the average speed.

  $\begin{array}{c}\overline{v}=\frac{d}{t}\\ =\frac{3220\text{ m}}{750\text{ s}}\\ =4.3\text{ m/s}\end{array}$

Conclusion:

Thus, the average speed of the person is $\text{4}\text{.3 m/s}$ .

(b)

To determine

The average velocity of the person.

Answer to Problem 9P

The average velocity of the person is $\text{0 m/s}$ .

Explanation of Solution

Given:

The number of complete laps

  $n=8$

Distance of one lap, $l=0.25\text{ mi}$

Total time taken, $t=12.5\text{ min}$

Formula used:

The average velocity of the person is given by,

  $v=\frac{\Delta x}{\Delta t}$    ……(3)

Calculation:

Displacement is the shortest distance between the starting and the ending point of the body’s motion. When the jogger completes a lap, he returns to exactly the same position he was when he had started. Therefore, at the end of 8 laps, the final and the initial positions of the jogger are the same.

Since displacement is defined as the difference between the body’s initial and final positions, the jogger’s displacement at the end of 8 laps is zero.

Hence, the jogger’s velocity at the end of 8 laps is also zero.

Conclusion:

Thus, the average velocity of the person is $\text{0 m/s}$ .