A car travelling 60km. /h Overtakes another car travelling at 42km./h. Asuming each car to be 5mtr. long . Find time taken during the Overtake. and road distance.

For the car with 60kmph to overtake the first car it should travel a relative distance of 10 m

(5m for catching up and 5m for getting clear ahead)

therefore Srel = 10 m

      Vrel = 60-42 = 18km/hr = 5 m/s

      Relative acceleration = 0 .since both are moving with constant velocities.

Now using relative motion,           S = Vrel × t

therefore time ,t = S / Vrel = 10/5 = 2s

Distance used to overtake is   60 × 5/18 × 2 = 100/3 = 33.33 m

As the second car overtakes the first one the total distance travelled by the second car will be 5m + 5m = 10m. 

Now, let the time taken to overtake the car be t seconds 

Therefore, 

distance travelled by seconds car in time t = distance travelled by first car in t + total overtaking distance, so

60t=42t+0.01

or

 t=1/1800hr or 2s 

Therefore time required to overtake the car is 2 seconds. 

Distance travelled in that time will be

 2s= 5 + 60*1/1800*1000

 =5+60/1.8 =5+33.33 

=38.33 m