Analyse velocity/time graphs to: a compare acceleration from gradients…

The idea

A velocity/time graph plots velocity on the vertical axis against time on the horizontal axis. The gradient of the line gives acceleration: a steeper line means greater acceleration, a horizontal line means zero acceleration (constant velocity), and a line sloping down means deceleration. To calculate acceleration for uniform acceleration, pick two points on a straight section and divide the change in velocity by the change in time, giving m/s². The area between the graph line and the time axis gives the distance travelled; for a straight-line section this area is a rectangle or triangle, so distance = area, in metres. For example, a triangle of base 4 s and height 10 m/s has area ½ × 4 × 10 = 20 m. Use gradient for acceleration and area for distance, and apply the calculation methods only where acceleration is uniform.

What earns the marks

• Compares gradients qualitatively, stating that a steeper gradient means greater acceleration.
• Calculates acceleration as the gradient, dividing change in velocity by change in time with unit m/s².
• Determines distance travelled from the area between the graph line and the time axis, in metres.
• Splits a compound area into rectangles and triangles and sums them to find total distance.
• Applies the gradient and area methods only to sections of uniform acceleration.
• Reads values from the axes accurately, including the time interval chosen for the gradient.

Common mistakes and how to put them right

• Reads the height of the line as distance.

  Put it right: Use the area under the line for distance and the gradient for acceleration.

• Divides time by velocity when finding the gradient.

  Put it right: Divide change in velocity by change in time.

• Treats a curved section as uniform acceleration.

  Put it right: Apply the calculation methods only to straight-line sections.

• Omits units or mixes them.

  Put it right: Give acceleration in m/s² and distance in m.

Exam tips

• Mark the two points you use for the gradient and show the change in velocity and change in time clearly.
• Shade the area you are calculating and label each rectangle or triangle before adding them.
• Check that a steeper line gives a larger acceleration value, as a quick sanity check.