Question

A body covers $\left(\frac{2}{5}\right)^{th}$ of the total distance with speed $v_{1}$ and $\left(\frac{3}{5}\right)^{th}$ with $v_{2}$ . The average speed of the body will be

• A. $\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$
• B. $\frac{v_{1} + v_{2}}{2}$
• C. $\frac{1}{2}\sqrt{v_{1} v_{2}}$
• D. $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

Answer 1

Answer: (A)

Let the total distance is $x,$ then we have
$t_{1}=\frac{2}{5} \, \frac{x}{v_{1}}$ and $t_{2}=\frac{3}{5} \, \frac{x}{v_{2}}$
Since, average speed, $v_{a v}=\frac{\text{total distance}}{\text{total time}}=\frac{x}{t_{1} + t_{2}}$
$=\frac{x}{\frac{2 x}{5 v_{1}} + \frac{3 x}{5 v_{2}}}=\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$
$\therefore \, v_{a v}=\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$