Question

A body covers one half of its journey at $40{\mathrm{ms}}^{-1}$and the next half at $50{\mathrm{ms}}^{-1}$. its average velocity is

• A. $44.4{\mathrm{ms}}^{-1}$
• B. $50{\mathrm{ms}}^{-1}$
• C. $45{\mathrm{ms}}^{-1}$
• D. $40{\mathrm{ms}}^{-1}$

Answer 1

The correct option is A

$44.4{\mathrm{ms}}^{-1}$

Step 1: Given:

1. A body covers one half of its journey at $40{\mathrm{ms}}^{-1}$
2. A body covers the next half at $50{\mathrm{ms}}^{-1}$

Let the total distance covered by the body be $s$

$$\begin{gathered} Time=\frac{Displacement}{Velocity} \\ Timeinhalfofjourney=\frac{{\displaystyle \raisebox{1ex}{$s$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{40}=\frac{s}{80}seconds. \\ Timeinnexthalfofjourney=\frac{{\displaystyle \raisebox{1ex}{$s$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{50}=\frac{s}{100}seconds. \end{gathered}$$

Finding average velocity:

Using the formula of average velocity,

$\mathrm{Average}\mathrm{velocity}=\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}\mathrm{taken}}$

$=\frac{\mathrm{s}}{{\displaystyle \frac{\mathrm{s}}{80}}+{\displaystyle \frac{\mathrm{s}}{100}}}=\frac{80\times 100}{180}=44.4{\mathrm{ms}}^{-1}$

Therefore the average velocity of the body is $44.4{\mathrm{ms}}^{-1}$

Hence, the correct option is (A).