A train stopping at two stations `2 km` apart on a straight line takes `4` minutes for the journey. Assuming that its motion its uniformly accelerated and then unoformly retarded. If `(1)/(x)+(1)/(y) = n`, where 'x' and 'y' are the magnitudesof the acceleration and retardation respectively. find the value of `n`.

Options

A. 2
B. `(1)/(2)`
C. 4
D. `(1)/(4)`

Answer

C

Explanation

Total time taken `= 4 min`
(i) `(v_0)/(x) + (v_0)/(y) = 4 min`
(ii) Total distance travelled `= 2 km`
`rArr` Area under `v-t` graph `= 2 km`
`(1)/(2) xx (v_0)/(x) xx v_0 + (1)/(2) xx (v_0)/(y) xx v_0 = 2 km`
From (i) and (ii), `(1)/(x)+(1)/(y) = 4`.