Speed time graphs

#### Tier: #Foundation #Higher

Description

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.

Links

Speed, distance & time Gradients as rates of change