Velocity-Time Graphs

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A velocity time graph, or velocity-time graph, shows how the velocity of a moving object varies with time
- Velocity-time refers to the fact that velocity is plotted against time on the graph
The red line represents an object with increasing velocity
The green line represents an object with decreasing velocity

Velocity-time graph

Velocity-Time Graph, downloadable IGCSE & GCSE Physics revision notes

Increasing and decreasing velocity represented on a velocity-time graph

Acceleration on a velocity-time graph

Velocity-time graphs also show the following information:
- Whether the object is moving with a constant acceleration
- The magnitude of the acceleration

A straight line represents constant acceleration (or deceleration)
The slope of the line represents the magnitude of acceleration
- A steep slope means large acceleration
  - The object's speed changes very quickly
- A gentle slope means small acceleration
  - The object's speed changes very gradually
- A positive gradient shows increasing velocity
  - The object is accelerating
- A negative gradient shows decreasing velocity
  - The object is decelerating
- A flat line means the acceleration is zero
  - The object is moving with a constant velocity

Constant acceleration and constant velocity on a velocity-time graph

velocity-time-graphs, IGCSE & GCSE Chemistry revision notes

Flat horizontal lines on a velocity-time graph show periods of constant velocity, and sloping straight line show periods of acceleration

Gradient of a velocity-time graph

How to find acceleration on a velocity-time graph

The acceleration of an object can be calculated from the gradient of a velocity-time graph

$acceleration = gradient = \frac{∆ y}{∆ x}$

velocity-time-gradient

How to find the gradient of a velocity-time graph

$∆ y$ is the change in $y$ (velocity) values
$∆ x$ is the change in $x$ (time) values

Worked example

A cyclist is training for a cycling tournament.

The velocity-time graph below shows the cyclist's motion as they cycle along a flat, straight road.

WE V-T graph Question image, downloadable IGCSE & GCSE Physics revision notes

(a) In which section (A, B, C, D, or E) of the velocity-time graph is the cyclist's acceleration the largest?

(b) Calculate the cyclist's acceleration between 5 and 10 seconds.

Answer:

Part (a)

Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration

The slope of a velocity-time graph indicates the magnitude of acceleration
Therefore, the only sections of the graph where the cyclist is accelerating are sections B and D
Sections A, C, and E are flat; in other words, the cyclist is moving at a constant velocity (therefore, not accelerating)

Step 2: Identify the section with the steepest slope

Section D of the graph has the steepest slope
Hence, the largest acceleration is shown in section D

Part (b)

Step 1: Recall that the gradient of a velocity-time graph gives the acceleration

Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period

Step 2: Draw a large gradient triangle at the appropriate section of the graph

A gradient triangle is drawn for the time period between 5 and 10 seconds

velocity-time-graph-we

Step 3: Calculate the size of the gradient and state this as the acceleration

The acceleration is given by the gradient, which can be calculated using:

$a = \frac{∆ y}{∆ x}$

$a = \frac{5}{5}$

$a = 1 m / s^{2}$

Therefore, the cyclist accelerated at 1 m/s² between 5 and 10 seconds

Examiner Tip

Use the entire slope, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used.

Remember to actually draw the lines directly on the graph itself, particularly when the question asks you to use the graph to calculate the acceleration.

Velocity-Time Graphs (Edexcel IGCSE Physics: Double Science)

Revision Note