Chapter 1, Problem 11P

To determine

The total distance travelled and average speed.

Explanation of Solution

Given:

The time interval of motion is $1.00\text{min}$ .

The following speeds are $0.400\text{km}/\text{min}$ , $0.240\text{km}/\text{min}$ , $0.160\text{km}/\text{min}$ , $0.160\text{km}/\text{min}$ and $0.320\text{km}/\text{min}$ .

Formula Used:

Speed is the distance covered in unit time by an object.

Write the expression for speed of an object.

  $v=\frac{d}{t}$

Here, $d$ is the distance covered, $t$ is the required time $v$ is the speed of object.

Rearrange the above expression in terms of $d$ .

  $d=vt$ ...... (I)

Write the expression for average speed.

  $v_{\text{avg}}=\frac{D}{T}$ ...... (II)

Here, $v_{\text{avg}}$ is the average speed, $D$ is the total distance travelled and $T$ is the total time.

Calculation:

Substitute $0.400\text{km}/\text{min}$ for $v$ and $1.00\text{min}$ for $t$ in equation (I).

  $\begin{array}{c}{d}_1=\left(0.400\text{km}/\text{min}\right)\left(1.00\text{min}\right)\\ =0.400\text{km}\end{array}$

Substitute $0.240\text{km}/\text{min}$ for $v$ and $1.00\text{min}$ for $t$ in equation (I).

  $\begin{array}{c}{d}_2=\left(0.240\text{km}/\text{min}\right)\left(1.00\text{min}\right)\\ =0.240\text{km}\end{array}$

Substitute $0.160\text{km}/\text{min}$ for $v$ and $1.00\text{min}$ for $t$ in equation (I).

  $\begin{array}{c}{d}_3=\left(0.160\text{km}/\text{min}\right)\left(1.00\text{min}\right)\\ =0.160\text{km}\end{array}$

Substitute $0.160\text{km}/\text{min}$ for $v$ and $1.00\text{min}$ for $t$ in equation (I).

  $\begin{array}{c}{d}_4=\left(0.160\text{km}/\text{min}\right)\left(1.00\text{min}\right)\\ =0.160\text{km}\end{array}$

Substitute $0.320\text{km}/\text{min}$ for $v$ and $1.00\text{min}$ for $t$ in equation (I).

  $\begin{array}{c}{d}_5=\left(0.320\text{km}/\text{min}\right)\left(1.00\text{min}\right)\\ =0.320\text{km}\end{array}$

Total distance travelled.

  $\begin{array}{c}D=0.400\text{km}+0.240\text{km}+0.160\text{km}+0.160\text{km}+0.320\text{km}\\ \text{=1}\text{.28}\text{km}\end{array}$

Total time taken.

  $\begin{array}{c}T=1.00\text{min}+1.00\text{min}+1.00\text{min}+1.00\text{min}+1.00\text{min}\\ \text{=5}\text{.00}\text{min}\end{array}$

Substitute $1.28\text{km}$ for $D$ and $5.00\text{min}$ for $T$ in equation (II).

  $\begin{array}{c}{v}_{\text{avg}}=\frac{1.28\text{km}}{5.00\text{min}}\\ =0.256\text{km}/\text{min}\end{array}$

Conclusion:

Thus, the total distance travelled is $1.28\text{km}$ and the average speed is $0.256\text{km}/\text{min}$ .