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 $ft = u$
$\therefore \quad t = \frac{u}{f}$
$S_{1} = ut = \frac{u^{2}}{f}$ and $S_{2} = \frac{1}{2} ft^{2} = \frac{u^{2}}{2f}$
$\therefore \quad S_{max} = S_{1}-S_{2} = \frac{u^{2}}{2f}$