Equations of Motion
Four equations link displacement, velocity, acceleration and time for constant acceleration.
About this topic
For constant acceleration, four equations connect 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 of the five variables, so choose the one missing what you don't need.
List the knowns, identify the unknown, and pick the equation that contains exactly those variables. Remember to set a positive direction and to use consistent units, for example metres and seconds. They apply only when acceleration is constant; for changing acceleration you need graphs or calculus.
Example: a car brakes from 20 m/s with a = -5 m/s² until it stops. Using v² = u² + 2as gives 0 = 400 - 10s, so s = 40 m. Using v = u + at gives t = 4 s. Accident investigators use the same method to estimate speeds from skid marks, and engineers use it to set safe following distances.
Tip: write down what the problem says in plain words, such as starts from rest meaning u = 0, or comes to a stop meaning v = 0. Falling objects and thrown balls also use these equations with a = g. Errors usually come from sign mistakes, so keep your signs consistent.
Key ideas
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
Quick check
Use cases: where Equations of Motion helps
- Homework: review the key idea behind Equations of Motion before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Equations of Motion without notes.
- Visual learning: play with the interactive lab to see how Equations of Motion changes when you adjust its inputs.
- Teaching a friend: explain Equations of Motion in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Equations of Motion?
Four equations link displacement, velocity, acceleration and time for constant acceleration.
What will I learn in Equations of Motion?
v = u + at. s = ut + ½at². v² = u² + 2as.
Is Equations of Motion part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Equations of Motion lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Equations of Motion?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.