Question

A man travels along a straight line. He covers the first half distance with constant velocity $v_1$ and the next half distance with constant velocity $v_2.$ The average velocity of man will be :

• A. $\frac{v_1+v_2}{2}$
• B. ${\left(v_1{v}_2\right)}^{1/2}$
• C. $v=\frac{2v_1{v}_2}{v_1+v_2}$
• D. ${\left(\frac{v_2}{v_1}\right)}^{1/2}$

Answer 1

Answer: (C)

Let Total distance = D

For, distance , $\frac{D}{2},V=V_1$

$t_1=\frac{D/2}{V_1}=D/2v_1$

For wxt $\frac{D}{2},V=V_2$

$t_2=\frac{D/2}{V_2}=D/2v_2$

average velocity = $\frac{Totaldistancetravelled}{Totaltime}$

$\frac{D}{\frac{D}{2V_1}+\frac{D}{2V_2}}=\frac{2V_1{V}_2}{V_1+V_2}$

average velocity = $\frac{2V_1{V}_2}{V_1+V_2}$