Velocity-time graphs Revision Notes for AQA GCSE Physics

Velocity-time graphs

Velocity-time graphs are useful tools that show how fast something is moving and how this speed changes over time. They help us understand motion and calculate important values like acceleration and distance.

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Velocity-time graphs are one of the most powerful tools in physics for analysing motion. They provide a visual representation that makes it easy to understand complex motion patterns at a glance.

What do velocity-time graphs show?

A velocity-time graph has:

Time on the x-axis (horizontal)
Velocity on the y-axis (vertical)

The graph shows you exactly how the velocity changes as time passes. This is really helpful for understanding different types of motion.

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Remember that velocity includes both speed and direction. On a velocity-time graph, positive values usually indicate movement in one direction, while negative values indicate movement in the opposite direction.

Reading velocity-time graphs

Different shapes on the graph mean different things:

Horizontal line: The object moves at constant velocity (steady speed). The velocity stays the same.

Sloping line upwards: The object is accelerating (speeding up). The steeper the slope, the faster it accelerates.

Sloping line downwards: The object is decelerating (slowing down). The steeper the slope, the faster it slows down.

Line on the x-axis (velocity = 0): The object is stationary (not moving).

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The steepness of the slope is crucial - it directly tells you how quickly the velocity is changing. A steep slope means rapid acceleration or deceleration, while a gentle slope indicates gradual changes in velocity.

Calculating acceleration from the graph

The gradient (slope) of a velocity-time graph tells you the acceleration.

Acceleration = change in velocity ÷ change in time

Or in mathematical notation: $a = \frac{\Delta v}{\Delta t}$

To find this:

Pick two points on the line
Work out the change in velocity (difference in y-values)
Work out the change in time (difference in x-values)
Divide change in velocity by change in time

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Worked Example: Calculating Acceleration

If velocity changes from 4 m/s to 10 m/s in 3 seconds:

Step 1: Find the change in velocity Change in velocity = $10 - 4 = 6 \text{ m/s}$

Step 2: Identify the change in time Change in time = $3 \text{ s}$

Step 3: Calculate acceleration Acceleration = $\frac{6 \text{ m/s}}{3 \text{ s}} = 2 \text{ m/s}^2$

Finding distance travelled

The area under the graph tells you the total distance travelled.

You can find this by:

Counting squares under the line
Using area formulas for shapes (rectangles, triangles)

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Worked Example: Calculating Distance

If the area under a graph section is 20 squares, and each square represents 5 metres:

Distance travelled = $20 \times 5 = 100 \text{ metres}$

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Always check the scale of your graph carefully. The value of each square depends on the scales used for both the time and velocity axes.

Real-world example

Imagine a train journey showing different phases of motion:

Stationary: Horizontal line at velocity = 0 (train stopped at station)
Accelerating: Line slopes upwards (train leaving station, speeding up)
Constant velocity: Horizontal line above zero (train travelling at steady speed)
Decelerating: Line slopes downwards (train slowing down to stop)

This real-world example shows how velocity-time graphs can tell the complete story of a journey, from start to finish.

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Key Points to Remember:

Gradient = acceleration - steeper slopes mean greater acceleration
Area under graph = distance - count squares to find how far travelled
Horizontal line = constant velocity - no change in speed
Upward slope = speeding up, downward slope = slowing down
Velocity-time graphs help you see the whole story of how something moves

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