Question

Two particles start moving from the same point along the same straight 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 greatest distance between the particle is

• A. $\frac{v^2}{a}$
• B. $\frac{v^2}{2a}$
• C. $\frac{2v^2}{a}$
• D. $\frac{v^2}{4a}$

Answer 1

Answer: (B)

Let $x$ be the distance between the particles after $t$ seconds. Then

$x=vt-\frac{1}{2}a{t}^2....(1)$

For $x$ to be maximum

$\frac{dx}{dt}=0$

or $v-at=0$

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

substituting this value in $(1)$ we get

$x=v(\frac{v}{a})-\frac{1}{2}a(\frac{v}{a}{)}^2$

or $x=\frac{v^2}{2a}$