Question

A person travels along a straight road for the first half time with a velocity, $v_1$ and the second half time with a velocity, $v_2$. Then the mean velocity $\overline{v}$ is given by:

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

Answer 1

The correct option is A $\overline{v}=\frac{v_1+v_2}{2}$

For the first half time$=t$, velocity$=v_1$, distance$=s_1=v_{1}t$
For the second half time$=t$, velocity$=v_2$, distance$=s_2=v_{2}t$
Mean velocity $=\frac{s_1+s_2}{t+t}=\frac{v_{1}t+v_{2}t}{2t}=\frac{v_1+v_2}{2}$