When a body moves with velocity `V_1` for first half of the journey and `V_2` for remaining half of the journey, its average velocity is given by `2/V_"av"=1/V_1+1/V_2` . If `V_1` and `V_2` are `(15pm0.5)` m/s and `(30pm0.1)` m/s, find the average velocity within error limits.

Explanation

It is given that `V_"av"=(2V_1V_2)/(V_1+V_2)`
First, we shall calculate `V_"av"`
`V_"av"=(2xx15xx30)/(15+30)`=20 m/s
Now, we shall calculate error in `V_"av"`
`2/V_"av"=1/V_1+1/V_2 `
`(2dV_"av")/V_a^2=(dV_1)/V_1^2+(dV_2)/V_2`
or `(2dV_"av")/400=0.5/225+0.1/900`
`dV_a=0.46`
`therefore V_"av"=(20pm0.4)`.