Question

A person travelling on a straight line moves with a uniform velocity $v_1$ for some time and with uniform velocity $v_2$ for the next equal time. The average velocity $v$ is given by:

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

Answer 1

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

Displacement during the velocity $v_1$ will be $x_1=v_{1}t$

Displacement during the velocity $v_2$ will be $x_2=v_{2}t$

Average velocity will be $\frac{Displacement}{time}=\frac{x_1+x_2}{t+t}=\frac{v_{1}t+v_{2}t}{2t}=\frac{v_1+v_2}{2}$

Option A is correct.