Determining Acceleration from V-T Graphs (SQA National 5 Physics): Revision Note

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.

(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 the significance of the gradient of a velocity-time graph

• The gradient of a velocity-time graph represents the magnitude (size) of the 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: 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 

Step 2: Calculate the size of the gradient and state this as the acceleration

• The acceleration is given by the gradient, which can be calculated using:

• Therefore, the cyclist accelerated at 1 m s^-2 between 5 and 10 seconds

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.