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

Hint: The average speed is defined as the total distance divided by the total time.

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

Time is taken to travel the first half distance $t_1=\frac{1/2}{v_1}=\frac{1}{2v_1}$
Time is taken to travel second half distance $t_2=\frac{1}{2v_2}$

Total time $t_1+t_2$ = $\frac{1}{2v_1}+\frac{1}{2v_2}$ = $\frac{1}{2}[\frac{1}{v_1}+\frac{1}{v_2}]$

Step 2: Find the average speed.

$We$ $know$ $that,$
$V_{avg}$ = Average velocity =  $\frac{total~distance}{total~ time}$
= $\frac{2v_1v_2}{v_1+v_2}$

Hence, option (3) is the correct answer.

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