Speed, Time, Distance and Trains
What you must know
The foundation is Distance = Speed × Time, with unit consistency: 1 km/h = 5/18 m/s, and 1 m/s = 18/5 km/h. Average speed is total distance ÷ total time, not the arithmetic mean of the speeds, unless the distances are equal - in which case the average is 2xy/(x+y).
Train problems fall into three patterns. (1) A train passing a stationary pole or person: distance = train length. (2) Passing a platform or bridge: distance = train length + platform length. (3) Two trains: same direction → relative speed is the difference; opposite directions → relative speed is the sum. Boats and streams use downstream speed = b + s and upstream = b − s.
Traps
- Mixing km/h with metres; convert before dividing.
- Using the arithmetic mean of speeds for a two-leg journey with equal distances (use 2xy/(x+y)) or unequal distances (use total distance/total time).
- Forgetting to add the train's own length when passing a platform.
- In relative-motion questions, subtracting speeds when the trains move in opposite directions.
- Late/early arrival problems: the time difference equals the difference of the two travel times.
Rule of thumb and example
Draw a small sketch with lengths and directions; label which distance is being covered.
Worked example: A 150 m train at 72 km/h crosses a 300 m platform. Speed = 72 × 5/18 = 20 m/s. Distance = 150 + 300 = 450 m. Time = 450/20 = 22.5 seconds.