A person travelling on a straight line moves with a uniform velocity `v_1` for a distance x and with a uniform velocity `v_2` for the next equal distance. The average velocity v is given by

Options

A. `v=sqrt(v_(1)v_(2))`
B. `(1)/(v)=(1)/(v_(1))+(1)/(v_(2))`
C. `(2)/(v)=(1)/(v_(1))+(1)/(v_(2))`
D. `(v)/(2)=(v_(1)+v_(2))/(2)`

Answer

c

Explanation

Let total distance be 2x. Particle moves distance x with speed `v_(1)` and remaining x with `v_(2)`. Let `t_(1)` and `t_(2)` be the time taken by the particle to cover corresponding distance.
As `t_(1)=(x)/(v_(1)` and `t_(2)=(x)/(v_(2))`
`therefore v=(x+x)/(t_(1)+t_(2))=(2x)/((x)/(v_(1))+(x)/(v_(2)))=(2v_(1)v_(2))/(v_(1)+v_(2))`
`therefore =(2)/(v)=(1)/(v_(1))+(1)/(v_(2))`