Speed, velocity and distance–time graphs
Distance and displacement
is how far an object moves. It is a : it has a size but no direction.
is the distance in a straight line from the start to the finish, and the direction. It is a .
Example: you run once round a 400 m track and finish where you started. The distance is 400 m, but your displacement is 0 m.
Key terms
Speed
Speed is rarely constant: it changes with fitness, age, the ground and how far you go. Typical values:
| Moving thing | Typical speed |
|---|---|
| Walking | 1.5 m/s |
| Running | 3 m/s |
| Cycling | 6 m/s |
| Sound in air | 330 m/s |
For constant (or average) speed, you must recall this equation:
, or s = vt
| Quantity | Symbol | Unit |
|---|---|---|
| Distance | s | metres (m) |
| Speed | v | metres per second (m/s) |
| Time | t | seconds (s) |
Example: a cyclist rides at 6 m/s for 5 minutes.
- Convert: 5 minutes = 300 s
- s = vt = 6 × 300
- s = 1800 m
Key terms
Velocity and circular motion (Higher tier only)
is , so it is a . "20 m/s" is a speed; "20 m/s north" is a velocity.
If the direction changes, the velocity changes, even if the speed stays the same.
An object moving in a circle at a constant speed has a changing velocity, because its direction is always changing. A satellite orbiting the Earth and a car going round a roundabout at a steady speed are both examples.
Key terms
Distance–time graphs
On a , distance goes up the side and time along the bottom. The (steepness) of the line is the .
- A straight sloping line: constant speed. Steeper means faster.
- A flat (horizontal) line: the object is stationary.
- A curve getting steeper: the object is speeding up.
Example: a line goes straight from 0 m to 120 m in 20 s.
speed = gradient = 120 ÷ 20 = 6 m/s
Higher tier: if the line is curved, find the speed at one moment by drawing a , a straight line that just touches the curve at that point. The gradient of the tangent is the speed at that moment.