MHT CET202520 Apr 2025Evening ShiftPhysicsMotion in One DimensionActual
Two bodies A and B move in same straight line starting from same position. Body A moves with constant velocity 'u' and body B moves with constant acceleration ' a '. When their velocities become equal, the distance between them is
Options
- Au 2 a
- Bu^2 4 a
- Cu ^2 a
- Du ^2 2 a
Correct answer
D. u ^2 2 a
Step-by-step solution
Define x=0 as the initial position at t=0 . Body A moves with constant velocity v_A = u , so its position is x_A = u t . Body B accelerates from rest with constant acceleration a , giving velocity v_B = a t and position x_B = 1 2 a t^2 . Equate their velocities to find when they are equal: u = a t , so t = u a . At this time, x_A = u u a = u^2 a and x_B = 1 2 a ( u a )^2 = u^2 2a . The distance between them is the absolute difference, which simplifies to D = | u^2 a - u^2 2a | = u^2 2a . The final answer is D .