Atrain Ais moving with a constant speed `v_A`. Its driver observes another train B in front of him on the san track and moving in the same direction with constant speed `v_B` If the distance between the trains be x, minimum retardation of the train A so as to avoid collision is
[The train A behind B comes to a halt]

Options

A. `((v_A+v_B)^2)/x`
B. `((v_A-v_B)^2)/x`
C. `((v_B+v_A)^2)/(2x)`
D. `((v_B-v_A)^2)/(2x)`

Answer

D

Explanation

`v_r^2-u_r^2 = 2a_rs_r implies 0-(v_B-v_A)^2 = 2ax, absa = ((v_B-v_A)^2)/(2x)`