Question

Two objects moving along the same straight line are leaving point $A$ with an acceleration $a,2a$ and 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. $\frac{3u^2}{a}$
• D. $\frac{4u^2}{a}$

Answer 1

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

Let both meet at point $B$.
Then from $2^{nd}$ equation of motion,
$s=ut+\frac{1}{2}a{t}^2$

For object 1:
$x=2ut+\frac{1}{2}a{t}^2...\left(i\right)$

For object 2:
$x=ut+\frac{1}{2}\left(2a\right)t^2...\left(ii\right)$

From (𝑖) and (𝑖𝑖)
$2ut+\frac{1}{2}a{t}^2=ut+a{t}^2$

$ut=\frac{1}{2}a{t}^2$

$\Rightarrow t=\frac{2u}{a}$

The distance moved by the object with respect to point $A$

$x=2u\left(\frac{2u}{a}\right)+\frac{1}{2}a(\frac{2u}{a}{)}^2$

$=\frac{6u^2}{a}$