Equations of Motion
The equations of motion link displacement, velocity, acceleration and time for objects moving with constant acceleration.
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The equations of motion link displacement, velocity, acceleration and time for objects moving with constant acceleration.
- v equals u plus a t
- s equals u t plus half a t squared
- v squared equals u squared plus 2 a s
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Equations of Motion?
Within Physics, which covers forces, energy, waves, electricity, magnetism, light and space explained through motion and experiments, this topic explains Equations of Motion. Physics topics explain how things move, push, heat up and carry energy, so each one here pairs a definition with a live model you can change.
Check that you can explain Equations of Motion in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Equations of Motion explains how the physical world behaves, from sport and transport to electricity and medicine.
Equations of Motion in detail
For constant acceleration, four equations link displacement s, initial velocity u, final velocity v, acceleration a and time t: v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Each omits one variable, so you choose the one that fits the information you have.
List the known and unknown quantities first, pay attention to signs for direction, and check units. These equations work only when acceleration is constant. They are used to analyse braking distances, falling objects and vehicles accelerating.
How the interactive helps you understand Equations of Motion
Watch the projectile path in the interactive. Use any sliders or buttons it offers to change the values and see how the projectile path responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Equations of Motion.
Real-life uses and examples
- Use Equations of Motion to make sense of a practical and its results.
- Answer “explain” questions by linking Equations of Motion to a clear cause and effect.
- Predict what a ball, car or circuit will do with Equations of Motion before you do the calculation.
Common mistakes to avoid
- Mixing up Equations of Motion with a related quantity that has different units.
- Forgetting that some quantities, such as force or velocity, also have a direction.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Equations of Motion
What is Equations of Motion?
The equations of motion link displacement, velocity, acceleration and time for objects moving with constant acceleration.
What are the most important points about Equations of Motion?
The main points are: v equals u plus a t; s equals u t plus half a t squared; v squared equals u squared plus 2 a s.
Why is Equations of Motion useful?
Understanding Equations of Motion explains how the physical world behaves, from sport and transport to electricity and medicine.
How can I practise Equations of Motion?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Equations of Motion?
Related topics in Physics include Newton's First Law, Mass and Weight, Resultant Forces.