Chapter 1, Problem 50P

(a)

To determine

The average speed of car.

Answer to Problem 50P

The average speed of car is $60.0\text{km}/\text{h}$ .

Explanation of Solution

Given:

The average speed of car is $80.0\text{km}/\text{h}$ in first hour and $40.0\text{km}/\text{h}$ in second hour.

Formula used:

Average speed is defined as total distance travelled by an object in unit time interval.

Write the expression for average speed.

  $v=\frac{d}{t}$ ...... (1)

Here, $d$ is the distance, $t$ is the time and $v$ is the average speed of object.

Rearrange the above expression in terms of $d$ .

  $d=vt$ ...... (2)

Calculation:

Substitute $80.0\text{km}/\text{h}$ for $v$ and $1.00\text{h}$ in equation (2).

  $\begin{array}{c}{d}_1=\left(80.0\text{km}/\text{h}\right)\left(1.00\text{h}\right)\\ =80.0\text{km}\end{array}$

Substitute $40.0\text{km}/\text{h}$ for $v$ and $1.00\text{h}$ in equation (2).

  $\begin{array}{c}{d}_2=\left(40.0\text{km}/\text{h}\right)\left(1.00\text{h}\right)\\ =40.0\text{km}\end{array}$

Calculate the total distance travelled by car.

  $\begin{array}{c}d=80.0\text{km}+40.0\text{km}\\ \text{=120}\text{km}\end{array}$

Calculate the total time taken by car.

  $\begin{array}{c}t=1.00\text{h}+1.00\text{h}\\ =\text{2}\text{.00}\text{h}\end{array}$

Substitute $120\text{km}$ for $d$ and $2.00\text{h}$ in equation (1).

  $\begin{array}{c}v=\frac{120\text{km}}{2.00\text{h}}\\ =60.0\text{km}/\text{h}\end{array}$

Conclusion:

Thus, the average speed of car is $60.0\text{km}/\text{h}$ .

(b)

To determine

The average speed of the car.

Answer to Problem 50P

The average speed of the car is $53.3\text{km}/\text{h}$ .

Explanation of Solution

Given:

The average speed in $1.00\text{km}$ is $80.0\text{km}/\text{h}$ and average speed in further $1.00\text{km}$ is $40.0\text{km}/\text{h}$ .

Formula used:

Rearrange the equation (II) in terms of $t$ .

  $t=\frac{d}{v}$ ...... (3)

Calculation:

Substitute $1.00\text{km}$ for $d$ and $80.0\text{km}/\text{h}$ for $v$ in equation (3).

  $\begin{array}{c}{t}_1=\frac{1.00\text{km}}{80.0\text{km}/\text{h}}\\ =\frac{1.00}{80.0}\text{h}\end{array}$

Substitute $1.00\text{km}$ for $d$ and $40.0\text{km}/\text{h}$ for $v$ in equation (3).

  $\begin{array}{c}{t}_2=\frac{1.00\text{km}}{40.0\text{km}/\text{h}}\\ =\frac{1.00}{40.0}\text{h}\end{array}$

Calculate the total distance travelled by car.

  $\begin{array}{c}d=1.00\text{km}+1.00\text{km}\\ \text{=2}\text{.00}\text{km}\end{array}$

Calculate the total time taken by car.

  $\begin{array}{c}t=\frac{1.00}{80.0}\text{h}+\frac{1.00}{40.0}\text{h}\\ \text{=}\frac{3.00}{80.0}\text{h}\end{array}$

Substitute $2.00\text{km}$ for $d$ and $\frac{3.00}{80.0}\text{h}$ for $t$ in equation (1).

  $\begin{array}{c}v=\frac{2.00\text{km}}{\left(\frac{3.00}{80.0}\text{h}\right)}\\ =53.3\text{km}/\text{h}\end{array}$

Conclusion:

Thus, the average speed of the car is $53.3\text{km}/\text{h}$ .