Revision: Graphs of velocity, acceleration, and displacement

1. Displacement-Time Graphs

• The slope of a displacement-time graph gives the velocity of an object.

• Formula for slope (velocity): $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\Delta x}{\Delta t} \quad \text{(m/s)}$

• The steeper the slope, the greater the velocity.

• A straight-line graph represents constant velocity.

2. Velocity-Time Graphs

• The slope of a velocity-time graph gives the acceleration of an object.

• Formula for slope (acceleration): $\text{slope} = \frac{\Delta v}{\Delta t} \quad \text{(m/s²)}$

• A horizontal line represents constant velocity (zero acceleration).

• A steeper slope means greater acceleration.

3. Displacement from a Velocity-Time Graph

• The area under a velocity-time graph represents the displacement of an object.
• Formula for displacement (area under graph): $\text{Area of a Triangle} = \frac{1}{2} \times \text{base} \times \text{height}$

$s = \frac{1}{2} \Delta t \times v$

• The larger the area, the greater the displacement.

4. Key Takeaways

• Gradient of a displacement-time graph = velocity.
• Gradient of a velocity-time graph = acceleration.
• Area under a velocity-time graph = displacement.
• Understanding these graphs helps in analysing motion effectively.