Ncert Exercises & Solutions

A vehicle travels half the distance $\mathrm{L} $ with speed $\mathrm{v_1}$ and the other half with speed $\mathrm{v_2},$ then its average speed is:
1. $\frac{v_{1} + v_{2}}{2}$

2. $\frac{2 v_{1} + v_{2}}{v_{1} + v_{2}}$

3. $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

4. $\frac{L (v_{1} + v_{2})}{v_{1} v_{2}}$

Step 1: Find the time taken by the vehicle in two cases.

Time is taken to travel the first half distance $t_{1} = \frac{l / 2}{v_{1}} = \frac{l}{2 v_{1}}$
Time is taken to travel second half distance $t_{2} = \frac{l}{2 v_{2}}$

$\begin{array}{l} Total time = \end{array}$ $t_{1} + t_{2}$ $= \frac{l}{2 v_{1}} + \frac{l}{2 v_{2}} = \frac{l}{2} [\frac{1}{v_{1}} + \frac{1}{v_{2}}]$

Step 2: Find the average speed.

$We$ $know$ $that,$ $V_{av} = Average speed = \frac{total distance}{total time}$
$=$ $\frac{l}{\frac{l}{2} [\frac{1}{v_{1}} + \frac{1}{v_{2}}]}$ $=$ $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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