Question

A bus and a car start from rest and run along a straight line with constant acceleration of $2m/s^2$ and $3m/s^2$ respectively, with the car behind the bus at distance of $100m$. How long in seconds will it take before both the bus and car travel side by side? Answer upto 2 decimal places

Answer 1

${\overrightarrow{a}}_{C.B}={\overrightarrow{a}}_C-{\overrightarrow{a}}_B={\overrightarrow{a}}_C+(-{\overrightarrow{a}}_B)=3-2=1m/s^2$
$\therefore |{\overrightarrow{a}}_{C.B}|=1m/s^2(\to )$ i.e ., relative acceleration = (constant)
$x_{rel}=u_{rel}t+\frac{1}{2}{a}_{rel}{t}^2\Rightarrow 100=0+\frac{1}{2}\times 1\times t^2$
$t=\sqrt{200}=10\sqrt{2}\text{sec}$