Question

A car travels a distance of $200\text{km}$ along a straight road at a speed of $40\text{km/h}$. The car returns back to same location with a speed of $60\text{km/h}$. Find the average speed and the average velocity of the car for the entire journey.

• A. Average speed $=48\text{km/h},$ Average velocity $=0\text{km/h}$
• B. Average speed $=24\text{km/h},$ Average velocity $=12\text{km/h}$
• C. Average speed $=48\text{km/h},$ Average velocity $=48\text{km/h}$
• D. Average speed $=24\text{km/h},$ Average velocity $=24\text{km/h}$

Answer 1

The correct option is A Average speed $=48\text{km/h},$ Average velocity $=0\text{km/h}$


Average speed $=\frac{\text{Total distance travelled}}{\text{Total time}}$
$=\frac{400\text{km}}{\frac{200\text{km}}{40\text{km/h}}+\frac{200\text{km}}{60\text{km/h}}}=\frac{400}{\frac{200}{10}(\frac{1}{4}+\frac{1}{6})}\text{km/h}$
$=\frac{20\times 24\text{km}}{(6+4)\text{h}}=48\text{km/h}$
Average velocity $=\frac{\text{Displacement}}{\text{Time taken}}=0$
Because displacement is zero.
Alternate method:
$V_{\text{av}}=\frac{2V_1{V}_2}{V_1+V_2}=\frac{2\times 40\times 60}{100}=48\text{km/h}$