A car trvelling at 60km/h overtakes another car travlling at 42km/h.Assuming each car to be 5.0m long.find the time taken during the overtake.
relative velocity=18km/hr, or 5m/s
time= distance/velocity= 1second
To find the time taken during the overtake, we need to consider the relative speed between the two cars.
The relative speed between the two cars is the difference between their speeds. In this case, the relative speed is:
Relative Speed = Speed of the overtaking car - Speed of the car being overtaken
Relative Speed = 60 km/h - 42 km/h
Relative Speed = 18 km/h
We need to convert the relative speed from kilometers per hour to meters per second, as the length of the cars is given in meters.
To convert kilometers per hour to meters per second, we use the following conversion factor:
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, the conversion factor is 1000/3600 = 5/18 (approximately 0.2778).
Now, we can calculate the relative speed in meters per second:
Relative Speed = 18 km/h * (5/18) m/s
Relative Speed = 5 m/s
Since the relative speed is the distance covered during the overtake divided by the time taken, we can rearrange the formula to calculate the time taken:
Time taken = Distance covered during the overtake / Relative Speed
The distance covered during the overtake is the sum of the lengths of both cars:
Distance covered during the overtake = Length of the overtaking car + Length of the car being overtaken
Distance covered during the overtake = 5.0 m + 5.0 m
Distance covered during the overtake = 10.0 m
Now, we can calculate the time taken:
Time taken = 10.0 m / 5 m/s
Time taken = 2 seconds
Therefore, the time taken during the overtake is 2 seconds.