Velocity-time graphs Revision Notes for AQA GCSE Physics Combined Science

Velocity-time graphs

What are velocity-time graphs?

Velocity-time graphs show how fast something is moving and how this speed changes over time. They are really useful for understanding motion and help us analyse different types of movement patterns.

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These graphs provide a visual way to analyse motion, making it easier to calculate acceleration and distance travelled from the motion data.

The graph has:

Time along the bottom (x-axis) - measured in seconds
Velocity up the side (y-axis) - measured in metres per second (m/s)

Reading different types of motion

You can tell what type of motion is happening by looking at the line on the graph. Each type of line represents a different motion pattern:

Horizontal line = moving at constant velocity (steady speed)
Sloping upward line = accelerating (getting faster)
Sloping downward line = decelerating (slowing down)
Line on the x-axis = stationary (not moving)

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The steeper the line, the greater the acceleration or deceleration. A very steep upward line means rapid acceleration, while a very steep downward line means rapid deceleration.

Finding acceleration from the slope

The slope (or gradient) of the line tells you the acceleration. This is one of the most important relationships in velocity-time graphs.

$\text{Acceleration} = \frac{\text{change in velocity}}{\text{change in time}}$

To calculate this:

Pick two points on the line
Work out the change in velocity between these points
Work out the change in time between these points
Divide the change in velocity by the change in time

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Worked Example: Calculating Acceleration

If velocity changes from 20 m/s to 10 m/s over 20 seconds:

Step 1: Calculate change in velocity Change in velocity = 10 - 20 = -10 m/s

Step 2: Identify change in time
Change in time = 20 seconds

Step 3: Apply the formula $\text{Acceleration} = \frac{-10}{20} = -0.5 \text{ m/s}^2$

The negative sign shows it's decelerating.

Finding distance travelled

You can work out the distance travelled by finding the area under the line. This is a powerful technique that works for any velocity-time graph.

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This works because distance = velocity × time, and the area under a velocity-time graph represents exactly this: velocity × time.

For simple shapes, you can use these formulas:

Rectangle = base × height
Triangle = $\frac{1}{2} \times \text{base} \times \text{height}$

You can also count the squares under the graph if you know what each square represents in terms of distance.

Worked example from the image

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Worked Example: Train Motion Analysis

A train's motion between 50s and 70s:

Given information:

Initial velocity = 20 m/s
Final velocity = 10 m/s
Time taken = 70s - 50s = 20s

Step 1: Calculate change in velocity Change in velocity = 10 - 20 = -10 m/s

Step 2: Apply acceleration formula $\text{Acceleration} = \frac{-10}{20} = -0.5 \text{ m/s}^2$

The negative value confirms the train is decelerating.

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Key Points to Remember:

Slope of the line = acceleration
Area under the line = distance travelled
Horizontal line = constant velocity
Upward slope = accelerating
Downward slope = decelerating

Velocity-time graphs (AQA GCSE Physics Combined Science): Revision Notes