Question

If a car covers $\frac{2}{5^{th}}$ of the total distance with $v_1$ speed and $\frac{3}{5^{th}}$ distance with $v_2$ then 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. $\frac{v_1{v}_2}{3v_1+2v_2}$

Answer 1

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

Average speed = $\frac{\text{Total distance travelled}}{\text{Total time taken}}$
$=\frac{x}{\frac{\frac{2x}{5}}{v_1}+\frac{\frac{3x}{5}}{v_2}}=\frac{5v_1{v}_2}{3v_1+2v_2}$