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Work & motion

Trains: measure the whole crossing

Choose the correct crossing distance and relative speed for poles, platforms and moving trains.

IntermediateAbout 13 min3 worked examples
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01 / THE STARTING POINT

Before you begin

What you need: Speed–distance–time and km/h to m/s conversion.

  • Distinguish crossing a point from a platform
  • Add train lengths for complete crossings
  • Use relative speeds in both directions
02 / BUILD THE CONCEPT

Understand the idea

The rear must clear the obstacle

To completely pass a pole, the front travels one train length from first contact. To clear a platform, it travels train length plus platform length.

Two trains contribute two lengths

For two trains to pass completely, their relative displacement must equal the sum of their lengths. This applies to both opposite-direction crossing and same-direction overtaking.

Relative speed depends on direction

For opposite directions, speeds add. For the same direction, use the positive difference between the faster and slower speeds. Equal speeds in the same direction do not produce an overtake.

03 / A DIFFERENT WAY TO SEE IT

Front enters → rear clears

Train: 120 m →Platform: 180 m
For a 120 m train and a 180 m platform, the front moves 300 m from first entry until the rear clears.
04 / FROM IDEA TO ANSWER

A method you can reuse

KEEP THIS HANDY

Crossing time = total length to clear ÷ relative speed

Use metres and m/s together; add both train lengths when two trains completely pass.
  1. Identify the object: point, platform or another train.
  2. Calculate the total distance the train must clear.
  3. Convert speeds, find relative speed if needed, and divide distance by speed.
A useful insight

Draw the front and rear at the beginning and end of the crossing. This often resolves whether one or two lengths are needed.

05 / WATCH THE METHOD WORK

Worked examples

Read the question first. Try a step yourself, then compare your reasoning.

EXAMPLE 01

Pass a pole

A 150 m train passes a pole at 54 km/h. Find the time.

  1. 54 × 5/18 = 15 m/s.
  2. The crossing distance is 150 m.
  3. Time = 150/15.
Answer10 seconds
EXAMPLE 02

Clear a platform

A 120 m train clears a 180 m platform at 72 km/h.

  1. Total distance = 120 + 180 = 300 m.
  2. 72 km/h = 20 m/s.
  3. Time = 300/20.
Answer15 seconds
EXAMPLE 03

Overtake another train

Trains of 100 m and 150 m travel at 72 and 54 km/h in the same direction. Find complete overtaking time.

  1. Relative speed = 18 km/h = 5 m/s.
  2. Combined length = 250 m.
  3. Time = 250/5.
Answer50 seconds
06 / YOUR TURN

Check your understanding

Quick questions, with explanations. These are for self-study and do not affect your account score.

0 of 3 questions checked

QUESTION 1An 80 m train clears a 120 m platform. Distance used?

See the explanation

200 m. Both train and platform lengths must be cleared: 80 + 120 = 200.

QUESTION 2Opposite-direction trains move at 40 and 50 km/h. Relative speed?

See the explanation

90 km/h. Their separation changes at the sum of their speeds.

QUESTION 3A 200 m train passes a pole in 10 seconds. Speed?

See the explanation

20 m/s. Speed = length/time = 200/10 = 20 m/s.

07 / TAKE THE NEXT STEP

Put your understanding to work

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EXPLORE THE NUMBERS

Train Crossing Calculator

Change the inputs and follow the working.

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Trains Practice Quiz 1

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Trains Practice Quiz 2

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Trains Practice Quiz 3

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