Velocity-Time Graphs | Physics for Grade 10 PDF Download

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

Exam Tip

Solved Example

Part (a)
Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration
(i) The slope of a velocity-time graph indicates the magnitude of acceleration
(ii) Therefore, the only sections of the graph where Tora is accelerating is section B and section D
(iii) 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
(i) 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
(i) 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
(i) The acceleration is given by the gradient, which can be calculated using:
acceleration = gradient = 5 ÷ 5 = 1 m/s²
(ii) Therefore, Tora accelerated at 1 m/s² between 5 and 10 seconds