SUVAT Equations

 What is SUVAT?  

- SUVAT is an acronym for the five quantities used when modelling motion in a straight line with constant acceleration:  

  - s: displacement from the starting point  

  - u: initial velocity  

  - v: final velocity  

  - a: acceleration  

  - t: time  

- All except time are vector quantities, meaning they can be positive or negative depending on direction.  

The Five SUVAT Equations  

1. v = u + at

2. v^2 = u^2 + 2as 

3. s = ut + 1/2at^2  

4. s = 1/2(u + v)t 

5. s = vt - 1/2at^2   

Derivation and Graphical Meaning  

- Four of these equations involve time and can be derived from a velocity–time graph.  

- With constant acceleration, the velocity–time graph is a straight line.  

- Acceleration is the gradient of the graph (found using differentiation).  

- Displacement is the area under the graph (found using integration).  

Common Exam Phrases  

- “Returns to its starting position” → s = 0  

- “Initially at rest” / “Stationary” → u = 0  

- “Comes to rest” → v = 0  

- “Falls freely” → a = g, where g is the acceleration due to gravity.