Question

Two objects are moving along the same straight line. They cross a point A with an acceleration $a$, $2a$ and velocity $2u$, $u$ at time $t=0$ respectively. The distance travelled by object when one overtakes the other is:

• A. $\frac{6u^2}{a}$
• B. $\frac{2u^2}{a}$
• C. $\frac{4u^2}{a}$
• D. $\frac{8u^2}{a}$

Answer 1

The correct option is C $\frac{4u^2}{a}$

Initially the object with velocity $2u$ will be ahead after t=0. Let's say they meet at time t. Thus distance covered by both will be equal in that period.

Distance covered by an object $S=ut+0.5a{t}^2$

Since distance covered by both the object in time $t$ are equal.

$\therefore$ $\left(2u\right)t+0.5\left(a\right)t^2=\left(u\right)t+0.5\left(2a\right)t^2$

Or, $a{t}^2-2ut=0$

$⟹t=\frac{2u}{a}$

Thus distance travelled by an object to overtake $S=ut+0.5a{t}^2=u\left(\frac{2u}{a}\right)+0.5a{\left(\frac{2u}{a}\right)}^2$

$⟹S=$$\frac{4u^2}{a}$