Interpreting Motion Graphs

This lesson covers distance-time graphs and velocity-time graphs — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to be able to interpret, draw and extract information from both types of graph, including calculating speed, acceleration and distance.

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Distance-Time Graphs

A distance-time graph plots the distance an object has travelled (y-axis) against the time taken (x-axis).

What the Shape Tells You

Shape of Graph	Meaning
Horizontal line	The object is stationary (not moving)
Straight line going up	The object is moving at constant speed
Steep straight line	Moving at a higher constant speed
Shallow straight line	Moving at a lower constant speed
Curve getting steeper	The object is accelerating (speeding up)
Curve getting shallower	The object is decelerating (slowing down)

Calculating Speed from a Distance-Time Graph

The gradient (slope) of a distance-time graph gives the speed:

Speed = Distance ÷ Time = Gradient of the line

For a straight line: choose two points, calculate rise ÷ run.

For a curved line: draw a tangent at the required point and calculate the gradient of the tangent.

Worked Example 1

A distance-time graph shows an object travels 120 m in 30 s in a straight line.

Speed = 120 / 30 = 4 m/s

Worked Example 2

On a distance-time graph, an object is at 50 m at t = 10 s and at 200 m at t = 40 s.

Speed = (200 − 50) / (40 − 10) = 150 / 30 = 5 m/s

Exam Tip: On a curved distance-time graph, you must draw a tangent (a straight line that just touches the curve) at the specific time you are interested in. Then calculate the gradient of the tangent. The Edexcel mark scheme awards separate marks for drawing the tangent correctly and for calculating the gradient.

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Velocity-Time Graphs

A velocity-time graph plots the velocity of an object (y-axis) against time (x-axis). These graphs give much more information than distance-time graphs.

What the Shape Tells You

Shape of Graph	Meaning
Horizontal line	Object moves at constant velocity (no acceleration)
Straight line going up	Constant acceleration (uniform acceleration)
Straight line going down (towards zero)	Constant deceleration (uniform deceleration)
Steep line	Greater acceleration (or deceleration)
Line at v = 0	Object is stationary
Curve	Changing acceleration (non-uniform)

Three Key Pieces of Information

1. Gradient = Acceleration

Acceleration = Change in velocity ÷ Time taken = Gradient

a = (v − u) / t

• Positive gradient → acceleration (speeding up)
• Negative gradient → deceleration (slowing down)
• Zero gradient → constant velocity

2. Area Under the Graph = Distance Travelled

The total area between the line and the time axis gives the total distance (or displacement) covered.

• For rectangles: area = base × height
• For triangles: area = ½ × base × height
• For trapeziums: area = ½ × (a + b) × h
• For irregular shapes, count the squares under the curve and multiply by what each square represents.

3. The y-value at any point gives the velocity at that time.

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Worked Examples: Velocity-Time Graphs

Worked Example 3: Calculating Acceleration

A car accelerates from 0 m/s to 20 m/s in 8 seconds.

a = (v − u) / t = (20 − 0) / 8 = 2.5 m/s²

Worked Example 4: Calculating Distance

The same car (0 to 20 m/s in 8 s) — what distance does it cover?

The graph forms a triangle:

Distance = ½ × base × height = ½ × 8 × 20 = 80 m

Worked Example 5: Multi-Stage Journey

A cyclist:

• Accelerates from 0 to 12 m/s in 6 s (triangle)
• Travels at 12 m/s for 10 s (rectangle)
• Decelerates from 12 m/s to 0 in 4 s (triangle)

Total distance:

• Stage 1: ½ × 6 × 12 = 36 m
• Stage 2: 10 × 12 = 120 m
• Stage 3: ½ × 4 × 12 = 24 m
• Total = 36 + 120 + 24 = 180 m

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Converting Between Graph Types

flowchart TD
    A["Distance-Time Graph"] -- "Gradient gives" --> B["Speed / Velocity"]
    B -- "Plot speed values<br/>against time" --> C["Velocity-Time Graph"]
    C -- "Area under graph gives" --> D["Distance"]
    D -- "Plot cumulative distance<br/>against time" --> A
    C -- "Gradient gives" --> E["Acceleration"]

    style A fill:#2980b9,color:#fff
    style B fill:#27ae60,color:#fff
    style C fill:#e67e22,color:#fff
    style D fill:#8e44ad,color:#fff
    style E fill:#c0392b,color:#fff

Key Relationships

From this graph...	You can find...	By calculating...
Distance-time	Speed	Gradient
Velocity-time	Acceleration	Gradient
Velocity-time	Distance	Area under the graph

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Real-World Examples

Example: A Car Journey

A car leaves home, drives to the shops, parks for a while, then drives back.

On a distance-time graph:

• Sloped line up = driving to the shops
• Horizontal line = parked at the shops
• Sloped line down (back to zero) = driving home

On a velocity-time graph:

• Line rising from zero = accelerating away from home
• Horizontal line = constant speed
• Line at zero = parked
• Line below zero or separate positive section = return journey

Example: A Ball Thrown Upward

On a velocity-time graph (taking upward as positive):

• Starts with a positive velocity (thrown upward)
• Velocity decreases (deceleration due to gravity)
• Velocity reaches zero (at the highest point)
• Velocity becomes negative (falling back down)
• Gradient is constant throughout (acceleration due to gravity, g ≈ 9.8 m/s² downward)

Exam Tip: When calculating area under a velocity-time graph, split the shape into simple rectangles and triangles. Show your working clearly — the Edexcel mark scheme awards marks for method even if the final answer is wrong.

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Common Mistakes

1. Confusing distance-time and velocity-time graphs. A straight line going up on a distance-time graph means constant speed, but on a velocity-time graph it means constant acceleration.

2. Forgetting that area under a distance-time graph has no useful physical meaning — only the area under a velocity-time graph gives distance.