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What Are the SUVAT Equations?
The SUVAT equations are a set of five kinematic equations that describe the motion of an object under constant (uniform) acceleration. The name comes from the five variables: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). These equations are fundamental to classical mechanics and are used extensively in physics education and engineering.
Given any three of the five variables, the remaining two can be calculated. This makes the SUVAT equations extremely versatile for solving problems involving projectile motion, free fall, vehicles accelerating or braking, and many other scenarios where acceleration is constant.
The Five SUVAT Equations
Variable Reference
| Symbol | Quantity | SI Unit |
|---|---|---|
| s | Displacement | meters (m) |
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | seconds (s) |
Worked Examples
Free-fall from 100 m
A ball is dropped from rest (u = 0) from 100 m height. With a = 9.81 m/s²: Using v² = u² + 2as, v = sqrt(2 x 9.81 x 100) = 44.3 m/s. Using s = ut + ½at²: t = sqrt(2s/a) = sqrt(200/9.81) = 4.52 s.
Frequently Asked Questions
When can I use SUVAT equations?
Only when acceleration is constant throughout the motion. If acceleration varies (e.g., air resistance, spring forces), you need calculus-based methods or numerical integration instead.
Can displacement be negative?
Yes. Displacement is a vector quantity. A negative displacement means the object moved in the negative direction from the reference point. Similarly, velocity and acceleration can be negative.
How do I handle projectile motion?
Split the motion into horizontal (a = 0) and vertical (a = -9.81 m/s²) components. Apply SUVAT equations independently to each direction. Time is the same for both components.