A car travelling on a straight track moves with a uniform velocity of v1 for some time and with uniform velocity v2 for the next equal time. The average velocity of the car is

Question

A car travelling on a straight track moves with a uniform velocity of v1 for some time and with uniform velocity v2 for the next equal time. The average velocity of the car is (A) √v1 v2 (B) (2 v1 v2/v1 + v2) (C) (v1 + v2/2) (D) (v1 - v2/2)

Tardigrade Admin · Accepted Answer

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

∴

Average velocity

= \frac{v _{1} t + v _{2} t}{t + t} = \frac{v _{1} + v _{2}}{2}

Q. 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

$v_{1} v_{2}$

$\frac{2 v _{1} v _{2}}{v _{1} + v _{2}}$

$\frac{v _{1} + v _{2}}{2}$

$\frac{v _{1} - v _{2}}{2}$

Q. A car travelling on a straight track moves with a uniform velocity of v1​ for some time and with uniform velocity v2​ for the next equal time. The average velocity of the car is

v1​v2​​

v1​+v2​2v1​v2​​

2v1​+v2​​

2v1​−v2​​

Q. 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

$v_{1} v_{2}$

$\frac{2 v _{1} v _{2}}{v _{1} + v _{2}}$

$\frac{v _{1} + v _{2}}{2}$

$\frac{v _{1} - v _{2}}{2}$