Speed and Distance–Time Graphs

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1. Key words

2. What is speed?

Speed tells you how fast something is moving: how much distance it covers in each unit of time. A car moving at 20 m/s travels 20 metres every second. To find a speed you need two measurements: the distance travelled and the time taken.

Rearranging. You can use the same three quantities to find distance or time. The formula triangle helps: cover the quantity you want and the triangle shows the calculation.

3. Units: change them first

Before you calculate, make the units match. If the question asks for m/s, the distance must be in metres and the time in seconds.

• 1 km = 1000 m (km → m: × 1000)
• 1 minute = 60 s (minutes → seconds: × 60)
• 1 hour = 60 minutes = 3600 s
• 30 minutes = 0.5 h; 15 minutes = 0.25 h; 20 minutes = 1/3 h

4. Average speed

Real journeys are never at one steady speed: cars stop at traffic lights and speed up again. Average speed treats the whole journey as if it were at one steady speed:

A speedometer shows the speed at one instant. An average speed can be much lower, because of the stops.

Measuring speed in the laboratory. To find the speed of a toy car: mark a start and a finish line a measured distance apart (for example 2.00 m, with a metre rule or tape measure); time the car between the lines with a stopwatch; repeat three times and calculate a mean time; then speed = distance ÷ mean time. Human reaction time makes stopwatch timings less accurate, especially for short times — light gates connected to a timer are more accurate.

5. Distance–time graphs

A distance–time graph shows a journey as a picture. Time goes along the horizontal axis (x-axis) and distance goes up the vertical axis (y-axis). The shape of the line tells you how the object is moving.

The gradient is the speed. For a straight section, speed = (change in distance) ÷ (change in time). Draw a right-angled triangle under the line, read the distance it rises and the time it covers, and divide.

• Start to A: the line slopes up steadily — constant speed. Speed = 100 m ÷ 20 s = 5 m/s.
• A to B: the line is flat — the cyclist is stationary for 30 − 20 = 10 s.
• B to C: steeper — faster. Speed = (300 − 100) m ÷ (50 − 30) s = 200 ÷ 20 = 10 m/s.
• C to D: flat — stationary again.
• Average speed for the whole 60 s = 300 m ÷ 60 s = 5 m/s.

6. Drawing a distance–time graph

1. Put time on the x-axis and distance on the y-axis (time is the independent variable).
2. Label each axis with the quantity and the unit, e.g. "time in s", "distance in m".
3. Choose a simple, even scale (1, 2, 5 or 10 per square) that uses more than half of the grid. Start both axes at 0.
4. Plot each point accurately with a small cross (×).
5. Join the points with straight lines using a ruler if the object moves at steady speeds; draw a smooth curve if the speed is changing.

7. Worked examples

Worked example 1 — A cheetah runs 210 m in 7 s. Calculate its speed. [2]

1. Write the formula: speed = distance ÷ time.
2. Substitute: speed = 210 ÷ 7.
3. Answer with unit: 30 m/s.
4. Common mistake: writing 7 ÷ 210 = 0.033. Always distance on top.

Worked example 2 — A car moves at a constant 25 m/s for 40 s. How far does it travel? [2]

1. distance = speed × time
2. = 25 × 40
3. = 1000 m (or 1 km)

Worked example 3 — An aeroplane flies 2400 km at an average speed of 800 km/h. How long does the flight take? [2]

1. time = distance ÷ speed
2. = 2400 ÷ 800
3. = 3 hours (the units km and km/h give hours)

Worked example 4 — Layla walks 900 m in 12 minutes. Calculate her average speed in m/s. [3]

1. Convert the time: 12 minutes × 60 = 720 s (1).
2. speed = 900 ÷ 720 (1)
3. = 1.25 m/s (1)
4. Common mistake: 900 ÷ 12 = 75 — that is 75 metres per minute, not m/s.

Worked example 5 — Use the cyclist graph in section 5. (a) Describe the motion between A and B. [1] (b) Which part of the journey is fastest? Explain how you can tell. [2]

1. (a) The cyclist is stationary (stopped) for 10 s — the line is horizontal.
2. (b) B to C (1), because that line is the steepest (1). (Check: 10 m/s compared with 5 m/s.)

Worked example 6 — A ball rolls down a slope. Its distance–time graph is a curve that gets steeper. Then it rolls along a flat floor and its graph becomes a curve that gets flatter until it is horizontal. Describe the motion. [3]

1. Down the slope: the ball is speeding up (the line gets steeper) (1).
2. On the floor: the ball is slowing down (the line gets less steep) (1)…
3. …until it stops (horizontal line) (1).

Practice

All pages in this course

Start here

• Stage 8 Science: The Tests and How to Prepare
• Thinking and Working Scientifically: Models, Investigations and Analysing Results

Biology

• Joints and Antagonistic Muscles
• Blood and Its Components
• Breathing, Gas Exchange and Diffusion in the Lungs
• A Balanced Diet, Energy Stores and Lifestyle
• Aerobic Respiration
• Ecosystems, Bioaccumulation and Invasive Species

Chemistry

• The Structure of the Atom
• Purity, Concentration and Chromatography
• Word Equations, Exothermic and Endothermic Reactions
• The Reactivity of Metals
• Impure Products and Solubility of Salts

Physics

• Speed and Distance–Time Graphs
• Balanced and Unbalanced Forces, and Moments
• Pressure, Particles and Diffusion
• Reflection and Refraction
• Dispersion and Colour
• Magnetic Fields and Electromagnets

Earth and space

• The Earth's Magnetic Field and Earth's Resources
• Climate, Weather and Climate Change
• Galaxies and Asteroids

Practice tests

• Stage 8 Science — Practice Test 1
• Stage 8 Science — Practice Test 2
• Stage 8 Science — Practice Test 3