Question

If a car covers $2/5^{\text{th}}$ of the total distance with $v_1$ speed and $3/5^{\text{th}}$ distance with $v_2$, then the average speed is -

• A. $\frac{1}{2}\sqrt{v_1{v}_2}$
• B. $\frac{v_1+v_2}{2}$
• C. $\frac{2v_1{v}_2}{v_1+v_2}$
• D. $\frac{5v_1{v}_2}{3v_1+2v_2}$

Answer 1

The correct option is D $\frac{5v_1{v}_2}{3v_1+2v_2}$

We know that, average speed,

$v_{\text{avg}}=\frac{\text{Total distance}}{\text{Total time}}$

$\Rightarrow v_{\text{avg}}=\frac{\frac{2}{5}s+\frac{3}{5}s}{\frac{2/5s}{v_1}+\frac{3/5s}{v_2}}$

$\Rightarrow v_{\text{avg}}=\frac{5v_1{v}_2}{3v_1+2v_2}$

Hence, option $\left(D\right)$ is the correct answer.