A body travels along a straight level road. For the first half time, its speed $v_{1}$ and for the second half time $v_{2}$ . What is the average speed ?What would be the average speed be if the first half distance covered with speed $v_{1}$ and the second half distance is covered with speed $v_{2}$ ?

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Solution

Given,

First half time speed is $V - 1$ and the second half speed is $V_{2}$

Let distance be $2 d$

For the first half $t_{1} = \frac{d}{V_{1}}$

For the second half $t_{2} = \frac{d}{V_{2}}$

So the total time is $t = t_{1} + t + 2$

$= \frac{d}{V_{1}} + \frac{d}{V_{2}}$

$d (\frac{v_{1} + v_{2}}{V_{1} V_{2}})$

Average speed is :

$\frac{2 d}{t_{1} + t_{2}}$

$= \frac{\frac{2 d}{d (V_{1} + V_{2})}}{V_{1} V_{2}}$

$= \frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

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