# Edexcel IGCSE Physics: Double Science 复习笔记： 1.1.5 Velocity-Time Graphs

### 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

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

• straight line represents constant acceleration
• The slope of the line represents the magnitude of acceleration
• steep slope means large acceleration (or deceleration) - i.e. the object's speed changes very quickly
• gentle slope means small acceleration (or deceleration) - i.e. the object's speed changes very gradually
• flat line means the acceleration is zero - i.e. the object is moving with a constant velocity

This image shows how to interpret 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

How to find 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 accelerationTherefore, 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 slope, 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!