Question

Two objects moving along the same straight line are leaving point $A$ with an acceleration $a$, $2a$ & velocity $2u$, $u$ respectively at time $t$ $=0$. The distance moved by the object with respect to point $A$ when one object overtakes the other is

• A. $\frac{6u^2}{a}$
• B. $\frac{2u^2}{a}$
• C. $\frac{4u^2}{a}$
• D. $noneofthese$

Answer 1

The correct option is A $\frac{6u^2}{a}$

Let both will meet at point B
$x=2ut+1/2a{t}^2$
$x=ut+\frac{1}{2}\left(2a\right)t^2$
So $2ut+\frac{1}{2}a{t}^2=ut+a{t}^2$
$ut=\frac{1}{2}a{t}^2\Rightarrow t=\frac{2u}{a}$
So $x=2u\left(\frac{2u}{a}\right)+\frac{1}{2}a{\left(\frac{2u}{a}\right)}^2=\frac{6u^2}{a}$