A body travelling along a straight line covers a distance's with a uniform speed y, If it covers the next distance s with a uniform speed, `v_2` then the average speed y of the body is

Options

A. `v=(v_1+v_2)/2`
B. `v=sqrt(v_1 v_2)`
C. `2/v = 1/v_1 +1/v_2`
D. `1/v = 1/v_1 +1/v_2`

Answer

C

Explanation

Let `t_1 " be time taken for s with " v_1 " Then " t_1= (s//v_1)`
Let `t_2 " be time taken for s with " v_2 " The " t_2= (s//v_2)`
The total time t is given by
`t=t_1+t_2=(s//v_1)+(s//v_2)=s(1/v_1 + 1/v_2)`
If v be average speed, then
`v=("total distance travelled"(2s))/("total time taken"(t)) ,v=(2s)/(s((1//v_1)+(1//v_2))) implies 2/v = 1/v_1 +1/v_2`