Formula and Method for the SUVAT Equations of Motion
SUVAT is a mnemonic for the five variables that describe motion under constant acceleration: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Because these five variables are linked by five interlocking equations, knowing any three of them is enough to solve for the other two — that is exactly what this calculator does.
The five SUVAT equations
Enter three known values and leave the other two fields blank. The calculator selects the correct pair of equations from the standard set and solves for the missing quantities:
- v = u + at — final velocity (no displacement needed)
- s = ut + ½at² — displacement (no final velocity needed)
- v² = u² + 2as — velocities and displacement (no time needed)
- s = ½(u + v)t — displacement from average velocity (no acceleration needed)
- s = vt − ½at² — displacement (no initial velocity needed)
Common mistakes
- Mixing sign conventions: pick one direction (e.g., "up" or "forward") as positive and keep it consistent — a decelerating object has acceleration with the opposite sign to its velocity.
- Applying SUVAT to non-uniform acceleration: these equations only hold when acceleration is constant; if it changes over time (e.g., air resistance at high speed), you need calculus-based kinematics instead.
- Forgetting units: SUVAT assumes SI units (meters, meters/second, meters/second², seconds) throughout — convert km/h to m/s (divide by 3.6) before entering a value.
Real-world applications
- Free-fall and projectile motion problems use a = -9.8 m/s² (or -32.2 ft/s²) for gravity near Earth's surface.
- Braking-distance estimates use a known (negative) deceleration and initial speed to find stopping distance s.
- Rocket and vehicle launches use SUVAT to relate thrust-driven acceleration to speed and distance covered.
- Introductory physics coursework (GCSE/A-level and university mechanics) uses SUVAT as the standard toolkit for constant-acceleration problems.
Frequently Asked Questions
What does SUVAT stand for?
SUVAT is an acronym for the five variables in the constant-acceleration equations of motion: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
What are the five SUVAT equations?
v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; and s = vt − ½at². Each equation omits exactly one of the five variables, so any three known values are enough to solve for the remaining two.
Do the SUVAT equations work if acceleration is not constant?
No. SUVAT only applies to motion with constant (uniform) acceleration. If acceleration changes over time, such as with air resistance at high speed, you need calculus-based kinematics instead of these algebraic equations.
How many values do I need to solve a SUVAT problem?
Exactly three of the five variables. With three known values, the standard equations combine to determine the remaining two unknowns, which is exactly what this calculator automates.