Question

A particle $X$ moving with a constant velocity $u$ crosses a point O. At the same instant another particle $F$ starts from rest from O with a constant acceleration $a$. The maximum separation between them before they meet is

• A. $u^2/2a$
• B. $u^2/a$
• C. $u/2a$
• D. $u/a$

Answer 1

The correct option is A $u^2/2a$

maximum distance will be when both of them have same velocity because after that point of time velocity of particle F will be more then that of particle X so distance between then starts decreasing.

$t=\frac{u}{a}$.

distance covered by X till this time is $S_1=u\times \frac{u}{a}$

distance covered by F till that time is $s_2=\frac{1}{2}a(\frac{u}{a}{)}^2=\frac{u^2}{2a}$

maximum distance between them $S_1-S_2=\frac{u^2}{2a}$

so option A is correct.