Question

Two bodies A and B move in the same straight line starting from the same position. Body A moves with constant velocity u and B moves with constant acceleration a. When their velocities become equal, the distance between them is ______.

Options

• `u^2/a`

• `(2u^2)/a`

• `u^2/(2a)`

• 2au²

Answer 1

Two bodies A and B move in the same straight line starting from the same position. Body A moves with constant velocity u and B moves with constant acceleration a. When their velocities become equal, the distance between them is `underlinebb(u^2/(2a))`.

Explanation:

The initial relative velocity of body A wrt body B,

v_AB = u - 0 = u

The relative acceleration of A wrt B,

a_AB = 0 - a = -a

According to the question, the velocity of A and B becomes equal, then,

v_AB = 0

⇒ `"v"_{AB}^2 - u_{AB}^2 = 2a_{AB}s ⇒ s = (0 - u^2)/(2(-a)) = u^2/(2a)`