Distance-time graphs Revision Notes for AQA GCSE Physics

Distance-time graphs

What are distance-time graphs?

Distance-time graphs are a way to show how an object moves. They help us understand the motion of vehicles, people, or any moving object.

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Understanding the axes is crucial for interpreting any distance-time graph correctly.

The axes:

Y-axis (vertical) = Distance (measured in metres)
X-axis (horizontal) = Time (measured in seconds)

The shape of the line tells us exactly how the object is moving.

Types of motion on distance-time graphs

Constant speed

Shape: Straight line sloping upwards
Meaning: The object moves at the same speed throughout
Example: A car driving at 30mph on a motorway

Accelerating (speeding up)

Shape: Curved line that gets steeper
Meaning: The object is going faster and faster
Example: A car pulling away from traffic lights

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Real-world Example: Accelerating Motion

Think of a cyclist starting from rest at traffic lights. Initially, they pedal slowly and cover little distance. As they build up speed, they cover more distance in each second, creating the characteristic curved line that gets steeper.

Decelerating (slowing down)

Shape: Curved line that gets less steep
Meaning: The object is getting slower
Example: A car approaching a red light

Stationary (not moving)

Shape: Horizontal flat line
Meaning: The object has stopped
Example: A car parked or waiting at traffic lights

Calculating speed from distance-time graphs

The speed of an object can be found by calculating the gradient (slope) of the line.

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Remember: On distance-time graphs, gradient = speed. This is a fundamental relationship you must understand.

Formula:

$\text{Speed} = \frac{\text{Change in distance}}{\text{Change in time}}$

How to calculate speed:

Pick two points on the line
Find the change in distance (vertical difference)
Find the change in time (horizontal difference)
Divide distance by time

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Worked Example: Calculating Speed

If a student walks 80m in 60 seconds:

Step 1: Identify the values

Change in distance = 80m
Change in time = 60s

Step 2: Apply the formula $\text{Speed} = \frac{80\text{m}}{60\text{s}} = 1.33 \text{ m/s}$

Answer: The student's speed is 1.33 m/s

Reading the graphs

Understanding the relationship between line characteristics and motion is essential:

Steeper lines = faster speed Gentle slopes = slower speed Horizontal lines = no movement

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The steepness of the line is directly proportional to the speed - the steeper the line, the faster the object is moving.

When the line curves:

Getting steeper = speeding up (accelerating)
Getting less steep = slowing down (decelerating)

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Common Mistake to Avoid:

Don't confuse distance-time graphs with speed-time graphs! On distance-time graphs:

The gradient tells you the speed
The shape tells you if speed is changing
A horizontal line means stationary (not constant speed)

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Key Points to Remember:

Distance goes on the y-axis, time on the x-axis
The gradient of the line tells you the speed
Straight lines = constant speed
Curved lines = changing speed (accelerating or decelerating)
Horizontal lines = the object is stationary (not moving)
Always check units and show your working in calculations

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