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A 628 m long train crosses a man walking at a speed of 10.1 km/h in the opposite direction in 12 seconds. What is the speed (in km/h) of the train?
179.3
178.3
180.2
180.6
179.3
Use the conversion factor 18/5 to go from m/s to km/h quickly. Since 628/12=52.33 m/s, convert to km/h by multiplying by 3.6 (or 18/5) and subtract the man's speed.
Train length L = 628 m, Man's speed Vm = 10.1 km/h, Time t = 12 s. Relative motion is in opposite direction.
Vrel=tL=Vt+Vm
Use the conversion factor 18/5 to go from m/s to km/h quickly. Since 628/12=52.33 m/s, convert to km/h by multiplying by 3.6 (or 18/5) and subtract the man's speed.
Forgetting that in opposite directions, the speeds of the train and the man are added, or failing to convert m/s to km/h correctly.
Calculate relative speed in m/s
The train covers its own length to cross the man. Using V=D/t, relative speed is 628/12 m/s.
Vrel=12628=52.333... m/s
Convert relative speed to km/h
Multiply the m/s value by 18/5 (or 3.6) to convert to km/h.
Vrel=52.333...×3.6=188.4 km/h
Calculate train speed
Since Vrel=Vtrain+Vman, we subtract the man's speed (10.1 km/h) from the relative speed.
Vt=188.4−10.1=178.3 km/h
B is correct because the calculated speed of the train is 178.3 km/h.
Always remember: same direction means subtract speeds, opposite direction means add speeds. This rule is identical for Relative Velocity in Physics Kinematics.