Question

A car is standing $200m$ behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2m/s^2$ and the car has acceleration $4m/s^2$. The car will catch up with the bus after a time of:

• A. $\sqrt{110}s$
• B. $\sqrt{120}s$
• C. $10\sqrt{2}s$
• D. $15s$

Answer 1

The correct option is C $10\sqrt{2}s$

Relative acceleration of car with respect to the bus is $4-2=2m/s^2$

Now initial distance is $200m$

as the Bus is taken as $reference$ so it can be treated as $rest$

So the situation is like this , $\text{A car with acceleration 2m/s^2 is approaching a stationary bus at a distance 200 m}$

So we can use $s=a{t}^2/2$ because initial velocity is $zero$.

So time $t=\sqrt[2]{22s/a}=14.14second$

We have used $s=200meter.$

Option C is correct.