Calculating Acceleration from Speed-Time Graphs (Cambridge O Level Physics)

Tora is training for a cycling tournament.

The speed-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 speed-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 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