Question

A car travelling on a straight track moves with a uniform velocity of $v_{1}$ for some time and with uniform velocity $v_{2}$ for the next equal time. The average velocity of the car is

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

Answer 1

Answer: (C)

Average velocity is equal to ratio of total displacement to total time. Velocity is a vector quantity and average velocity is defined as the total displacement undergone by the body per unit time.
Displacement in first instance $=v_{1}t$
Displacement in second instance $=v_{2}t$
$\therefore \, $ Average velocity $=\frac{v_{1} t + v_{2} t}{t + t}=\frac{v_{1} + v_{2}}{2}$