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

Answer

D

Explanation

Since `v^2 = u^2 + 2ax rArr ax = (v^2 - u^2)/(2)`
At C `v_c^2 + u^2 + 2a (x/2) rArr v_c^2 = u^2 + (v^2 - u^2)/(2)`
`rArr v_c = sqrt((v^2+u^2)/(2))`