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Two trains of length 220┬аm and 280┬аm are running towards each other on parallel lines at 42┬аkm/h and 30┬аkm/h, respectively. In how much time will they be clear of each other from the moment they meet?
21 sec
25 sec
20 sec
10 sec
25 sec
Convert speed from km/h to m/s by multiplying by 5/18. Total length is 220+280=500 m, relative speed is 72 km/h, which is 72├Ч5/18=20 m/s. Time =500/20=25 seconds.
Length of train 1 = 220 m, Length of train 2 = 280 m, Speed 1 = 42 km/h, Speed 2 = 30 km/h
T=S1тАЛ+S2тАЛD1тАЛ+D2тАЛтАЛ
Convert speed from km/h to m/s by multiplying by 5/18. Total length is 220+280=500 m, relative speed is 72 km/h, which is 72├Ч5/18=20 m/s. Time =500/20=25 seconds.
Forgetting to convert relative speed from km/h to m/s, or simply adding the speeds without unit conversion.
Calculate Total Distance
Since the trains are moving towards each other, the total distance to be covered to clear each other is the sum of their lengths.
DtotalтАЛ=220+280=500┬аm
Calculate Relative Speed
Since the trains are moving in opposite directions, their relative speed is the sum of their individual speeds.
SrelтАЛ=42+30=72┬аkm/h
Convert Speed to m/s
To match the units of distance (meters) and time (seconds), convert 72 km/h to m/s.
SrelтАЛ=72├Ч185тАЛ=20┬аm/s
Calculate Time
Use the time formula T=D/S to find the time taken.
T=20500тАЛ=25┬аseconds
B is correct because the total distance of 500 m covered at a relative speed of 20 m/s results in exactly 25 seconds.
This concept of relative speed is fundamental in kinematics and is frequently tested in problems involving objects in motion, such as overtaking or crossing in trains and boats.
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