Question

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

• A. \(\frac{\mathrm{u}}{2\mathrm{a}}\)
• B. \(\frac{\mathrm{u}^{2}}{4\mathrm{a}}\)
• C. \(\frac{\mathrm{u}^{2}}{\mathrm{a}}\)
• D. \(\frac{\mathrm{u}^{2}}{2\mathrm{a}}\)

Hint:

Find the time when B reaches velocity u, then compare the distances covered by each body in that time.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Body A moves at constant speed \(u\). Body B starts from rest at the same point with acceleration \(a\).

Step 2: Time when speeds are equal
\(u=at\Rightarrow t=\dfrac{u}{a}\).

Step 3: Distances
A: \(s_A=ut=\dfrac{u^2}{a}\).
B: \(s_B=\dfrac{1}{2}at^2=\dfrac{u^2}{2a}\).

Step 4: Separation
\(s_A-s_B=\dfrac{u^2}{a}-\dfrac{u^2}{2a}=\dfrac{u^2}{2a}\).

Final Answer:
The separation is u squared over 2a. \[ \boxed{\text{(D) }\dfrac{\mathrm{u}^{2}}{2\mathrm{a}}} \]