Question

Two particles move in the same straight line starting from the same position. The first moves with constant velocity u and the second with constant acceleration f. During the time elapses before the second catches the first greatest distance between the particles is

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

Answer 1

Answer: (B)

The greatest distance is, when velocities of both are equal.
or $ft=u$
$\therefore t=\frac{u}{f}$
$S_1=ut=\frac{u^2}{f}$ and $S_2=\frac{1}{2}f{t}^2=\frac{u^2}{2f}$
$\therefore S_{max}=S_1-S_2=\frac{u^2}{2f}$