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Work & motion

Speed, distance & time: connect the units

Relate distance to travel time, convert units, and calculate average speed for an entire journey.

IntermediateAbout 14 min3 worked examples
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01 / THE STARTING POINT

Before you begin

What you need: Division, fractions and unit conversion.

  • Use distance = speed × time
  • Convert km/h to m/s and back
  • Find average speed from total distance and time
02 / BUILD THE CONCEPT

Understand the idea

Speed tells distance per unit time

At a constant 60 km/h, a traveller covers 60 km each hour. The equation d = vt connects distance d, speed v and elapsed time t.

Units must fit together

If speed is in km/h, distance must be in kilometres and time in hours. Multiply km/h by 5/18 to obtain m/s because 1 km is 1000 m and 1 hour is 3600 seconds.

Average speed is a journey ratio

Average speed equals total distance divided by total time, including stops if they are part of the elapsed journey. The simple mean of two speeds works for equal time intervals, not generally for equal distances.

03 / A DIFFERENT WAY TO SEE IT

An equal-distance return trip

  1. 60 km at 30 km/h
  2. Outward time: 2 h
  3. 60 km at 60 km/h
  4. Return time: 1 h
Total distance 120 km ÷ total time 3 h = 40 km/h average, not 45 km/h.
04 / FROM IDEA TO ANSWER

A method you can reuse

KEEP THIS HANDY

v = d/t; d = v × t; t = d/v

Average speed = total distance ÷ total elapsed time.
  1. Convert distances and times to compatible units.
  2. Choose the rearrangement that isolates the required value.
  3. For multiple stages, add distances and times separately before dividing.
A useful insight

For two equal nonzero distances at positive speeds u and v, average speed = 2uv/(u + v). It follows by adding the two travel times.

05 / WATCH THE METHOD WORK

Worked examples

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

EXAMPLE 01

Find travel time

How long does 150 km take at 60 km/h?

  1. t = d/v = 150/60.
  2. 2.5 hours = 2 hours + 0.5 hour.
  3. 0.5 hour = 30 minutes.
Answer2 hours 30 minutes
EXAMPLE 02

Convert speed

Convert 72 km/h to m/s.

  1. 72 km/h = 72000 metres per 3600 seconds.
  2. Equivalently, multiply 72 by 5/18.
  3. 72 × 5/18 = 20.
Answer20 m/s
EXAMPLE 03

Average speed

Travel 60 km at 30 km/h, then 60 km at 60 km/h. Find average speed.

  1. First time = 2 hours; second time = 1 hour.
  2. Total distance = 120 km; time = 3 hours.
  3. 120/3 = 40.
Answer40 km/h
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 1Distance travelled at 45 km/h for 2 hours?

See the explanation

90 km. d = 45 × 2 = 90 km.

QUESTION 2Convert 10 m/s to km/h.

See the explanation

36 km/h. Multiply by 18/5: 10 × 18/5 = 36.

QUESTION 3A 100 km journey takes 2 hours driving and 30 minutes stopped. Overall average?

See the explanation

40 km/h. Total elapsed time is 2.5 hours; 100/2.5 = 40 km/h.

07 / TAKE THE NEXT STEP

Put your understanding to work

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EXPLORE THE NUMBERS

Speed, Distance and Time Calculator

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Speed Distance and Time Practice Quiz 1

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Speed Distance and Time Practice Quiz 2

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Speed Distance and Time Practice Quiz 3

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Speed, distance and time practice

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