# 5.6.11 Velocity-Time Graphs

### Gradient of a Velocity-Time Graph

• A velocity-time graph shows how the velocity of a moving object varies with time
• The red line represents an object with increasing velocity
• The green line represents an object with decreasing velocity Increasing and decreasing velocity represented on a velocity-time graph

#### Acceleration on a Velocity-Time Graph

• Velocity-time graphs also show the following information:
• If the object is moving with a constant acceleration/deceleration
• The magnitude of the acceleration/deceleration
• A straight line represents constant acceleration
• The slope of the line represents the magnitude of acceleration
• A steep slope means large acceleration (or deceleration) – i.e. the object’s speed changes very quickly
• A gentle slope means small acceleration (or deceleration) – i.e. the object’s speed changes very gradually
• A flat line means the acceleration is zero – i.e. the object is moving with a constant velocity Interpreting the slope of a velocity-time graph

#### Calculating the Gradient of a Velocity-Time Graph

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

#### Worked Example

Tora is training for a cycling tournament.
The velocity-time graph below shows her motion as she cycles along a flat, straight road. (a) In which section (A, B, C, D, or E) of the velocity-time graph is Tora’s acceleration the largest?
(b) Calculate Tora’s acceleration between 5 and 10 seconds.

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 Tora is accelerating is section B and section D
• Sections A, C, and E are flat – in other words, Tora is moving at a constant velocity (i.e. 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 below: 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:

acceleration = gradient = 5 ÷ 5 = 1 m/s2

• Therefore, Tora accelerated at 1 m/s2 between 5 and 10 seconds

#### Exam Tip

Use the entire line, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used – so remember to draw ‘rise’ and ‘run’ lines directly on the graph itself! ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
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