Forces and Motion — Distance, Speed and VelocityAQA GCSE Physics: Revision notes
Section 1
What Is the Difference Between Distance and Displacement?
- Distance is a scalar quantity — how far an object has travelled, regardless of direction.
- Displacement is a vector quantity — how far an object has travelled from its starting point in a straight line, including the direction.
Displacement is expressed as a magnitude and a direction, e.g. '5 m east'.
A runner completes one full lap of a 400 m track. The distance travelled is 400 m, but the displacement is 0 m because they end up back where they started.
Section 2
How Fast Do Things Typically Move?
It is useful to know some typical everyday speeds:
| Activity | Typical speed |
|---|---|
| Walking | ~1.5 m/s |
| Running | ~3 m/s |
| Cycling | ~6 m/s |
| Speed of sound in air | ~330 m/s |
Section 3
How Do You Calculate Speed?
Speed is a scalar quantity describing how fast an object is moving. Distance travelled equals speed multiplied by time, so speed = distance ÷ time.
For a journey where speed changes, you calculate the average speed using the total distance travelled divided by the total time taken — this smooths out any variation during the journey.
A cyclist travels 12 km in 40 minutes (2400 s). Average speed = 12000 m ÷ 2400 s = 5 m/s.
Section 4
What Is Velocity, and How Is It Different From Speed?
Velocity is speed in a given direction — it is a vector quantity, whereas speed is a scalar.
This distinction matters: an object moving at constant speed around a circular track has a continuously changing velocity, because its direction is constantly changing, even though its speed stays the same. The same speed–velocity, distance–displacement distinction applies throughout mechanics.
Do not treat 'speed' and 'velocity' as interchangeable in an exam answer — examiners look for the direction/vector distinction when a question specifically asks about velocity.
Section 5
How Do You Read a Distance–Time Graph?
On a distance–time graph:
- The gradient (slope) of the line represents speed — a steeper line means a faster speed.
- A horizontal line means the object is stationary (speed = 0).
- A curved line means the object's speed is changing (accelerating or decelerating).
- (HT) To find the speed of an accelerating object at one particular instant, draw a tangent to the curve at that point and calculate the gradient of the tangent.
Always check the units on both axes before reading off a gradient as a speed — mixing up minutes and seconds is a common mistake.
Must Know
- Distance (scalar) has no direction; displacement (vector) is distance from the start point plus direction.
- Typical speeds: walking ~1.5 m/s, running ~3 m/s, cycling ~6 m/s, sound in air ~330 m/s.
- Speed = distance ÷ time; average speed = total distance ÷ total time.
- Velocity is speed in a given direction — a vector, unlike speed.
- On a distance–time graph, gradient = speed; a horizontal line means stationary; a curve means changing speed.
- (HT) The speed of an accelerating object at an instant is found from the gradient of a tangent to the distance–time curve.
That's the notes covered.
Carry on to the next subtopic.