A speed-time graph shows how an object's speed changes over time. The shape of the graph tells you about the object's motion.
Key features:
- Horizontal line: constant speed (no acceleration)
- Positive gradient (rising): acceleration
- Negative gradient (falling): deceleration
- Area under graph: distance travelled
Finding distance: calculate the area under the graph using the shapes formed (triangles, rectangles, trapezoids). $$\text{Distance} = \text{area under the speed-time graph}$$
Example: A car accelerates from 0 to $20\text{ m/s}$ in 5 seconds, then travels at constant speed for 10 seconds.
- Area of triangle: $\frac{1}{2} \times 5 \times 20 = 50\text{ m}$
- Area of rectangle: $10 \times 20 = 200\text{ m}$
- Total distance: $250\text{ m}$
Gradient of a speed-time graph = acceleration (in m/s²).
Common error: finding distance from a distance-time graph by reading area rather than gradient — the two graphs have opposite interpretations.