A car travelling at 60 km/h overtakes another car travelling at 42 km/h. Assuming each car to be 5m long, find the time taken during the overtake and the total road distance used for the overtake.
Answers
Solution :
Car A speed =60km/hr=60x5/18=50/3 m/s
Car B speed =42km/hr=42x5/18=35/3 m/s
Relative speed of Car A w.r.t Car B is =50/3 - 35/3=15/3=5 m/s
Total distance to be covered in overtaking = Length of both cars =10m
Time =Distance/speed=10m/5m/s=2 sec
Total distance used for overatking will be equal to distance covered by car in overtaking + length of car
=(50/3)x2+5
=100/3 +5
=33.3+5
=38.3 m
∴time taken during the overtake and the total road distance used for the overtake is 38.3m
Speed of the first car = 60 km/h
Speed of second car= 42 km/h
So, the relative speed of first car with respect to second car = 60-42 =18 km/h
To convert km/h to m/s we multiply the Speed in km/h by 5/18 .
So, relative speed = 18 × (5/18) = 5 m/s.
Now, as the first car overtakes the second car, it has to cover the second car's length as well it's own length. Understand it : the front part of the first car will first cover the length of second car and then the rear part of first car will cover the length of second car.
Thus, in order to overtake, the first car covers a distance = 5+5 = 10m
So, time taken = (10/5) second = 2 second.
Now, in order to calculate road distance, time remains same in every frame in this case. Thus, the total road distance covered by first car = (Speed of 1st car)×(time taken in overtake) = (60 x (5/18))×2 m = 33.3 m
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