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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
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