Question

Two particles start moving from the same point along the same stright line. The first moves with constant velocity v and the second with constant acceleration a. During the time that elapses before the second catches the first, the greater distance between the particles is

• A. $\frac{v^2}{a}$
• B. $\frac{v^2}{2a}$
• C. $\frac{2v^2}{a}$
• D. $\frac{v^2}{3a}$

Answer 1

The correct option is B $\frac{v^2}{2a}$

A distance between the two particles is maximum when both have the same velocity

let the second move has a velocity v at time t

$v=at$

$t=\frac{v}{a}$

distance cover by the first paticle $s_1$ is

= $s_1=vt=v\times \frac{v}{a}=\frac{v^2}{a}$

distance cover the particle $s_2$

$=\frac{1}{2}\times a{t}^2=\frac{v^2}{2a}$

distance between both the particle is

$s_1-s_2$

$=\frac{v^2}{a}-\frac{v^2}{2a}=\frac{v^2}{2a}$

hence the B option is correct