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).
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses