Motion
Speed, distance and time
Speed and average speed
Speed is the distance travelled per unit time. It is a scalar quantity (magnitude only, no direction).
\[ \text{speed} = \frac{\text{distance}}{\text{time}} \quad\Rightarrow\quad v = \frac{d}{t} \]
SI unit: metres per second (m/s). Also used: km/h, cm/s.
Average speed is calculated over a whole journey — it does not tell you whether the object was speeding up, slowing down, or stationary at any particular moment.
\[ \text{average speed} = \frac{\text{total distance}}{\text{total time}} \]
Worked example — average speed calculation
A car travels 120 km in 1.5 hours. Calculate its average speed in m/s.
Step 1: Convert units. \( d = 120\,\text{km} = 120\,000\,\text{m} \); \( t = 1.5\,\text{h} = 1.5 \times 3600 = 5400\,\text{s} \).
Step 2: Apply the formula. \( v = \dfrac{d}{t} = \dfrac{120\,000}{5400} = 22.2\,\text{m/s} \)
Distance-time graphs
A distance-time (d-t) graph shows how far an object has travelled from its starting point at each moment in time.
- Gradient = speed. A steeper slope means a higher speed.
- Horizontal line → the object is stationary (distance not changing).
- Straight line with positive slope → constant speed.
- Curve becoming steeper → the object is speeding up (accelerating).
- Curve becoming shallower → the object is slowing down (decelerating).
Calculating speed from a d-t graph
To find the speed from a straight section of a d-t graph:
\[ \text{speed} = \text{gradient} = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1} \]
Choose two clearly readable points on the line (not data points — use the line itself). Draw a large triangle to minimise reading error.
Worked example — speed from gradient
On a distance-time graph, a straight line passes through (0 s, 0 m) and (4 s, 24 m). Find the speed.
\( v = \dfrac{\Delta d}{\Delta t} = \dfrac{24 - 0}{4 - 0} = \dfrac{24}{4} = 6\,\text{m/s} \)
When you calculate the gradient, always show the two coordinates you used and the unit in your final answer. The examiner awards the mark for the correct unit (m/s) — writing just "6" without the unit loses the mark.
A d-t graph cannot show negative distance in the basic IGCSE context (distance is a scalar and is always ≥ 0). If the graph line goes back down towards the x-axis, the question has plotted a displacement-time graph instead — mention this distinction if the question asks you to comment.
Useful unit conversions
| From | To | Multiply by |
|---|---|---|
| km/h | m/s | ÷ 3.6 |
| m/s | km/h | × 3.6 |
| cm/s | m/s | ÷ 100 |
| minutes | seconds | × 60 |
| hours | seconds | × 3600 |