Calculating Acceleration from Speed-Time Graphs (CIE IGCSE Physics)

EXTENDED 

• If there is a change in an object's speed, then it is accelerating

• An object may accelerate at a steady rate, this is called constant acceleration
  • On a speed-time graph this will be a non-horizontal straight line

• An object may accelerate at an increasing rate
  • On a speed-time graph this would be an upward curve with an increasing gradient

• An object may accelerate at a decreasing rate
  • On a speed-time graph this would be an upward curve with a decreasing gradient
    
    

• An object is said to decelerate if its speed is decreasing over time, i.e. its acceleration is negative 
  • On a speed-time graph this would be a downward line
    • If the line is a non-horizontal straight line, deceleration is constant
    • If the line is a curve with an increasing gradient, deceleration is increasing
    • If the line is a curve with a decreasing gradient, deceleration is decreasing

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

 

How to find the gradient of a speed-time graph

Part (a)

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

• • The slope of a speed-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 speed (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 speed-time graph gives the acceleration

• • Calculating the gradient of a slope on a speed-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