Question

A body goes from A to B with a speed of $60\mathrm{Km}/\mathrm{h}$and then returns to the starting point with a speed of $40\mathrm{Km}/\mathrm{h}$.

Find (a) the average speed

(b) the average velocity of the body.

Answer 1

Step 1: Given data

Initial speed $\left({\mathrm{v}}_1\right)=60\mathrm{Km}/\mathrm{h}$

Final speed $\left({\mathrm{v}}_2\right)=40\mathrm{Km}/\mathrm{h}$

Step 2: Formula Used

As we need to calculate the average speed (${\mathrm{v}}_{\mathrm{av}}$) and average velocity ($\overrightarrow{{\mathrm{v}}_{\mathrm{av}}}$)for the whole journey, the formulas used will be:

${\mathrm{v}}_{\mathrm{av}}=\frac{{\mathrm{v}}_1+{\mathrm{v}}_2}{2}$

$\overrightarrow{{\mathrm{v}}_{\mathrm{av}}}=\frac{Totaldisplacement}{Totaltime}$

Step 3: Calculation of average speed (${\mathrm{v}}_{\mathrm{av}}$) for the whole journey

${\mathrm{v}}_{\mathrm{av}}=\frac{60\mathrm{Km}/\mathrm{h}+40\mathrm{Km}/\mathrm{h}}{2}$

${\mathrm{v}}_{\mathrm{av}}=\frac{100}{2}$

${\mathrm{v}}_{\mathrm{av}}=50\mathrm{Km}/\mathrm{h}$

Step 4: Calculation of average velocity ($\overrightarrow{{\mathrm{v}}_{\mathrm{av}}}$) for the whole journey

As the body returns to the point from where it started, the total displacement will be zero.

$\overrightarrow{{\mathrm{v}}_{\mathrm{av}}}=\frac{0}{2}$

$\overrightarrow{{\mathrm{v}}_{\mathrm{av}}}=0$

Therefore, if a body goes from A to B with a speed of $60\mathrm{Km}/\mathrm{h}$ and then returns to the starting point with a speed of$40\mathrm{Km}/\mathrm{h}$, then (a) the average speed will be $50\mathrm{Km}/\mathrm{h}$ and (b) the average velocity of the body will be zero.