Question

Two points move in the same straight line starting at the same moment from the same point. One moves with velocity \(u\) and the other with acceleration \(f\). The greatest distance between them is:

• A. \( \frac{u}{f} \)
• B. \( \frac{u^2}{2f} \)
• C. \( \frac{f}{2u^2} \)
• D. \( \frac{f}{u^2} \)

Hint:

Maximum separation occurs when relative velocity becomes zero.

Answer 1

The Correct Option is B

Concept: Relative motion: \[ \text{Distance} = ut - \frac{1}{2}ft^2 \]

Step 1:Max distance when velocity difference = 0} \[ \frac{d}{dt}(ut - \frac{1}{2}ft^2) = 0 \Rightarrow u - ft = 0 \Rightarrow t = \frac{u}{f} \]

Step 2:Substitute:} \[ s = u\cdot \frac{u}{f} - \frac{1}{2}f\cdot \left(\frac{u}{f}\right)^2 \] \[ = \frac{u^2}{f} - \frac{1}{2}\frac{u^2}{f} = \frac{u^2}{2f} \]