Question

A bus starts from rest with a constant acceleration of 5m/s². At the same time a car traveling with a constant velocity of 50m/s overtakes and passes the bus. (i) Find at what distance will the bus overtakes the car? (ii) How fast will the bus be travelling then?

Answer 1

Let=Time to overtake(i)Condition to overtake:Distance travelled by car = Distance travelled by busut+12at2car=ut+12at2bus0t+125t2car=50t+120t2bus2.5t2=50t2.5t=50t=20 sHence,distance=ut =50×20 =1000 m(ii)Velocity of bus:v=at =5×20 =100 m/s