1. Tardigrade
  2. Question
  3. Physics
  4. A bus starts from rest with a constant acceleration of 5 m s -2. At the same time a car travelling with constant velocity of 50 m s -1 passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed?

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Q. A bus starts from rest with a constant acceleration of $5 \,m\, s ^{-2}$. At the same time a car travelling with constant velocity of $50 \,m \,s ^{-1}$ passes the bus. Assuming that the car passes the bus at the instant the bus is starting when the bus overtakes the car, what is its speed?

Motion in a Straight Line

Solution:

Let the bus overtake the car after time $t$ at distance $s$.
Using the relation, $s=u t+\frac{1}{2} a t^{2}$
For bus, $s=0+\frac{1}{2} \times 5 \times t^{2}$
For car, $s=50 t ; $
$ \therefore \frac{5}{2} t^{2}=50 t$ or $t=20 s$
If $v$ is the velocity of the bus after time $t$, then
$v=0+5 \times 20=100 m s ^{-1}$