Velocity-Time Graphs

The area under the line of a velocity-time graph represents the displacement (or total distance travelled in a specific direction). This is because displacement is the product of velocity and time ($s = v \times t$).

For motion with constant acceleration, the area usually forms simple geometric shapes. You can calculate the total displacement by summing the areas of these shapes:

• Rectangles: Used for periods of constant velocity ($Area = \text{base} \times \text{height}$).

• Triangles: Used for periods of uniform acceleration starting or ending at rest ($Area = \frac{1}{2} \times \text{base} \times \text{height}$).

If the graph is a curve, the acceleration is non-uniform. In such cases, displacement must be estimated by counting the squares underneath the curve on the grid and multiplying by the value of a single square.

Check the Axes and Units: Always verify the units on both axes before calculating. If time is in minutes or distance in kilometres, convert them to standard SI units ($s$ and $m$) to ensure the acceleration is in $m/s^2$.

Use Large Gradient Triangles: When calculating the slope, draw a large triangle on the graph. This reduces the percentage error in your readings and is often a requirement for gaining full marks in practical-based questions.

Sanity Check the Area: When calculating displacement, ensure you have accounted for the entire area down to the x-axis ($v=0$). Students often mistakenly stop at the lowest point of the line rather than the axis itself.

Describe Motion Precisely: Use terms like 'uniform acceleration', 'constant velocity', and 'deceleration' rather than just 'speeding up' or 'moving' to demonstrate technical proficiency.