Velocity-Time Graphs

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

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:
- 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

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

Interpreting the slope of a velocity-time graph

Gradient of a Velocity-Time Graph

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

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

velocity-time-gradient

The gradient of a velocity-time graph can be found by dividing the change in velocity by the change in time

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 GCSE Physics: Combined Science)

Revision Note