(a) A particle moving with constant acceleration from `A` to `B` in a straight line `AB` has velocities `u` and `v` at `A` and `B` respectively. Find the velocity of the particle at the midpoint of `AB`.
(b) If the time taken by the particle to go from `A` to the midpoint of `AB` is two times that from the midpoint of `AB` to `B` then find the value of `v//u`.

Options

A. `((u^(2)+v^(2))/2)^(2)`
B. `(u^(2)+v^(2))/2`
C. `(v-u)/2`
D. `sqrt((u^(2)+v^(2))/2)`

Answer

D

Explanation

`A` to `B`: `V^(2)=u^(2)+2a.d/2 …(i)`
`A` to `C`: `v^(2)=u^(2)+2a.d …(ii)`
From (ii), `ad=(v^(2)-u^(2))/2` in (i)
`V^(2)=u^(2)+(v^(2)-u^(2))/2=(v^(2)+u^(2))/2`
`V=sqrt((v^(2)+u^(2))/2)`