Shortcut Trick
Relative speed in m/s = Distance ÷ Time = 150 ÷ 3 = 50 m/s.
Convert to km/h: 50 × (18 ÷ 5) = 180 km/h.
Since both are moving in the same direction, Relative Speed = Train Speed − Man Speed.
Train Speed = 180 + 2 = 182 km/h.
∴ The correct answer is 182 km/h.
Alternate Method
Given:
Length of train = 150 m
Time taken to pass the man = 3 s
Speed of man = 2 km/h (moving in the same direction)
Formula Used:
Relative Speed = Total Distance ÷ Time
Relative Speed (same direction) = Speed of Train − Speed of Man
Speed in km/h = Speed in m/s × (18 ÷ 5)
Calculations:
⇒ Relative Speed = 150 ÷ 3 = 50 m/s
⇒ Convert relative speed to km/h: 50 × (18 ÷ 5) = 180 km/h
⇒ Let the speed of the train be v km/h.
⇒ Relative Speed = v − 2
⇒ v − 2 = 180
⇒ v = 180 + 2 = 182 km/h
∴ The correct answer is 182 km/h.
Additional Information
Relative Speed (Same Direction)
When two bodies are moving in the same direction, their relative speed is calculated by taking the difference of their individual speeds (V1 − V2).
Relative Speed (Opposite Direction)
When two bodies are moving in opposite directions, their relative speed is calculated by adding their individual speeds (V1 + V2).
Speed Unit Conversion
To convert a speed from m/s to km/h, multiply the value by 18 ÷ 5. To convert from km/h to m/s, multiply the value by 5 ÷ 18.
Train Passing a Point Object
When a train completely passes a man, tree, or pole, the total distance covered by the train is strictly equal to the length of the train itself.