Speed, velocity and distance-time graphs
Speed tells you how fast; velocity adds the direction. A distance-time graph shows a whole journey at a glance, and its slope tells you the speed at each moment.
Part 1 of 3: Learn it
In short
- Distance and speed are scalars; displacement and velocity are vectors.
- distance travelled = speed × time (s = vt).
- On a distance-time graph, the gradient is the speed and a flat line means stationary.
Where this is in your specification
Spec points: AQA 4.5.6.1.1 to 4.5.6.1.4 (Combined Trilogy 6.5.4.1.1 to 6.5.4.1.4), Edexcel Topic 2, OCR P2.1
| Board | Topic: Forces and motion |
|---|---|
| AQA 8463 | 4.5.6 (8463); 6.5.4 (8464) |
| Edexcel 1PH0 | Topic 2 |
| OCR J249 | P2.1 and P2.2 |
| Eduqas C420 | 4.1 to 4.3 |
| Cambridge IGCSE 0625 | 1.2, 1.5 |
| National 5 C857 75 | Dynamics: vectors and scalars, velocity-time graphs, acceleration |
Scalars and vectors in motion
Distance is how far something travels along its path; displacement is how far it ends up from the start, in a straight line, with a direction. A runner who does one lap of a 400 m track has covered 400 m but has a displacement of zero.
In the same way, an object moving in a circle at a steady speed has a changing velocity, because its direction keeps changing.
Typical speeds
| Moving thing | Typical speed |
|---|---|
| Walking | about 1.5 m/s |
| Running | about 3 m/s |
| Cycling | about 6 m/s |
| Car in town | about 13 m/s |
| Sound in air | about 330 m/s |
Real speeds vary with age, fitness, wind and terrain. Questions may ask you to estimate one, so these are worth knowing.
Reading distance-time graphs
- A straight sloping line: constant speed. The steeper, the faster.
- A horizontal line: the object is not moving.
- A curve getting steeper: speeding up. A curve getting flatter: slowing down.
- Speed = gradient = change in distance ÷ change in time.
Speed on a curve (Higher)
If the line is curved, draw a tangent: a straight line that just touches the curve at the point you want. The gradient of the tangent is the speed at that instant.
What is a typical walking speed?
Show the answer
About 1.5 m/s.
Part 2 of 3: See it worked
Worked examples
Example 1
A graph shows a jogger covering 120 m in the first 40 s at a steady rate. What is her speed?
- Gradient = 120 ÷ 40
Answer: 3 m/s.
Example 2
A tangent to a curved distance-time graph passes through (2 s, 0 m) and (8 s, 30 m). Find the speed at that point. (Higher)
- Change in distance = 30 − 0 = 30 m
- Change in time = 8 − 2 = 6 s
- Gradient = 30 ÷ 6
Answer: 5 m/s.
Example 3
A cyclist rides at 6 m/s for 15 minutes. How far does she go?
- t = 15 × 60 = 900 s
- s = v × t = 6 × 900
Answer: 5400 m (5.4 km).
Common mistakes
- Reading a flat line as constant speed. It means stopped.
- Using minutes in s = vt when the speed is in m/s.
- Saying an object going round a circle at steady speed has constant velocity.
- Finding the gradient of a curve from two far-apart points instead of a tangent.
On a distance-time graph, what does a steeper straight line show?
Show the answer
A greater constant speed.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
What is a typical walking speed?
About 1.5 m/s.
On a distance-time graph, what does a steeper straight line show?
A greater constant speed.
A car travels 2.4 km in 3 minutes. Find its average speed in m/s.
2400 m ÷ 180 s = 13.3 m/s.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Ces fiches sont en anglais car elles suivent les programmes d'examen britanniques.
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses