Question

A person travels along a straight road for the first $\frac{t}{3}$ time with a speed $v_{1}$ and for next $\frac{2 t}{3}$ time with a speed $v_{2}$. Then the mean speed $v$ is given by

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

Answer 1

Answer: (A)

$v_{ av }=\frac{\text { Distance }}{\text { Time}}=\frac{\text { Speed } \times \text { Time }}{\text { Time }}$
$=\frac{v_{1} \times \frac{t}{3}+v_{2} \times \frac{2 t}{3}}{\frac{t}{3}+\frac{2 t}{3}}$
$\Rightarrow v_{ av }=\frac{\frac{v_{1}}{3}+\frac{2 v_{2}}{3}}{1}=\frac{v_{1}+2 v_{2}}{3}$
$\Rightarrow v_{ av }=\frac{v_{1}+2 v_{2}}{3}$