Acceleration: The following equation applies to uniform acceleration:

The idea

This statement introduces the condition for using the kinematic equation v² − u² = 2 × a × s: acceleration must be uniform, meaning it stays constant in magnitude and direction throughout the motion. Uniform acceleration produces a straight-line velocity–time graph, so the gradient is constant. For example, a ball rolling down a smooth slope may be modelled as uniform acceleration, but a car in stop-start traffic is not. When acceleration is uniform, average velocity is (u + v) / 2 and distance is that average multiplied by time. If acceleration changes, the equation cannot be applied directly; the motion must be split into stages or a graph used. Recognising this condition is part of choosing the correct equation.

What earns the marks

• Define uniform acceleration as constant acceleration in magnitude and direction, giving a straight-line velocity–time graph.
• Explain that v² − u² = 2 × a × s is valid only when acceleration is uniform, and state what happens if it is not.
• Use the gradient of a velocity–time graph to check whether acceleration is constant before selecting the equation.
• Apply the equation to a described uniform-acceleration stage, such as a vehicle braking steadily or a trolley accelerating down a ramp.
• Recognise that average velocity (u + v) / 2 can be used only for uniform acceleration, linking this to distance = average velocity × time.

Common mistakes and how to put them right

• Assuming any motion with changing speed has uniform acceleration.

  Put it right: Uniform acceleration requires a constant rate of change of velocity, shown by a straight velocity–time line.

• Using v² − u² = 2 × a × s for a whole journey that includes different acceleration stages.

  Put it right: Split the journey into stages where acceleration is uniform.

• Confusing uniform acceleration with constant speed.

  Put it right: Constant speed means a = 0, while uniform acceleration means a is constant and non-zero.

Exam tips

• Look for words such as steadily, uniformly or constant acceleration in the question before using the equation.
• Sketch a velocity–time graph to confirm the gradient is constant; this justifies your choice of equation.
• If acceleration changes, state that the equation applies only to each uniform stage and calculate stage by stage.