Speed Conversion (km/h ↔ m/s)

Statement

Speed can be expressed in different units depending on context. Everyday travel often uses kilometres per hour (km/h), while physics calculations usually use metres per second (m/s). The two are related by the factor 3.6:

\[ \text{m/s} = \frac{\text{km/h}}{3.6}, \quad \text{km/h} = 3.6 \times \text{m/s} \]

Why it’s true

• 1 kilometre = 1000 metres.
• 1 hour = 3600 seconds.
• So, \(1 \,\text{km/h} = \tfrac{1000}{3600} \,\text{m/s} = \tfrac{1}{3.6}\,\text{m/s}\).
• Reversing gives \(1 \,\text{m/s} = 3.6 \,\text{km/h}\).

Recipe (how to use it)

1. To convert from km/h to m/s, divide by 3.6.
2. To convert from m/s to km/h, multiply by 3.6.
3. Always check the units in the question: physics formulae (e.g. \( v = d/t \)) usually expect m/s.

Spotting it

Look for word problems where speeds are mixed with distances in metres or times in seconds. Unit consistency is essential for correct answers.

Common pairings

• Formulae for speed, distance, and time (\(v = d/t\)).
• Kinematics equations in physics.
• Car speed limits and running paces in real-life problems.

Mini examples

1. Given: Convert 72 km/h to m/s. Answer: \(72 \div 3.6 = 20\) m/s.
2. Given: Convert 15 m/s to km/h. Answer: \(15 \times 3.6 = 54\) km/h.

Pitfalls

• Forgetting whether to divide or multiply by 3.6.
• Mixing up km and m, or hours and seconds.
• Rounding too early instead of keeping exact decimals until the end.
• Leaving the answer without units.

Exam strategy

• Underline the units in the question.
• Write down the conversion formula before substituting.
• Check the reasonableness of your answer: 100 km/h is about 28 m/s, so answers far off this scale are suspect.

Summary

Converting between km/h and m/s is a straightforward calculation using the factor 3.6. Divide by 3.6 to go to m/s, multiply by 3.6 to go to km/h. This skill is critical for accuracy in GCSE physics and applied maths problems involving motion.