MECHANICSKinematicsPhysics Calculator
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SUVAT Kinematic Equations

SUVAT equations describe uniformly accelerated motion. Five variables: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Given any three, the other two can be found.

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v = u + at (no displacement) s = ut + ½at² (no final velocity) v² = u² + 2as (no time) s = ½(u+v)t (no acceleration)

Key quantities
Velocity-time
v = u + at
Key relation
Displacement
s = ut + ½at²
Key relation
Velocity-displacement
v² = u² + 2as
Key relation
Average velocity
s = ½(u+v)t
Key relation

Ready to run the numbers?

Why: SUVAT equations are fundamental to kinematics. Used for projectile motion, free fall, braking distance, and any constant-acceleration scenario.

How: Select exactly 3 known variables. The calculator applies the appropriate equation(s) to solve for unknowns. All five equations are equivalent—any three variables determine the system.

v = u + at (no displacement)s = ut + ½at² (no final velocity)
Sources:NIST Physical ConstantsMIT OCW Physics

Run the calculator when you are ready.

Solve SUVAT EquationsSelect 3 known variables to find the other 2

📐 The Five SUVAT Equations

v = u + ext{at}

Final velocity from initial velocity, acceleration, and time

s = ext{ut} + ½ ext{at}^{2}

Displacement from initial velocity, acceleration, and time

s = ext{vt} - ½ ext{at}^{2}

Displacement from final velocity, acceleration, and time

v^{2} = u^{2} + 2as

Final velocity from initial velocity, acceleration, and displacement

s = ½(u + v)t

Displacement from average velocity and time

⚙️ SUVAT Variables

Instructions: Select exactly 3 known variables (highlighted in blue). The calculator will solve for the other 2.

s

Displacement

u

Initial Velocity

v

Final Velocity

a

Acceleration

t

Time

suvat-calculator@bloomberg:~$
VELOCITY: LOW
s (m)
100.00
u (m/s)
0.00
v (m/s)
20.00
a (m/s²)
2.00
t (s)
10.00

✅ Complete SUVAT Solution

s (Displacement)
100.00
meters
u (Initial)
0.00
m/s
v (Final)
20.00
m/s
a (Acceleration)
2.00
m/s²
t (Time)
10.00
seconds

Equations Applied:

t = (v - u) / as = ut + ½at²
Motion Type
Accelerating
Average Velocity
10.00 m/s
Velocity Change
20.00 m/s
Distance
100.00 m

📈 Motion Visualization

📏 Position vs Time

s = ut + ½at² visualization

🚀 Velocity vs Time

v = u + at (linear relationship)

📊 SUVAT Values Comparison

⚡ Kinetic Energy (per kg)

📝 Step-by-Step Solution

📊 Known Variables

Initial Velocity (u): 0.00 m/s

Final Velocity (v): 20.00 m/s

Acceleration (a): 2.00 m/s²

🧮 SUVAT Solution

Using t = (v - u) / a

t = (20.00 - 0.00) / 2.00

→ t = 10.0000 s

Using s = ut + ½at²

s = (0.00 × 10.00) + (0.5 × 2.00 × 10.00²)

→ s = 100.0000 m

📈 Derived Quantities

Average Velocity: v_avg = (u + v) / 2

→ v_avg = 10.0000 m/s

Velocity Change: Δv = v - u

→ Δv = 20.0000 m/s

Motion Type: Accelerating

📖 What is SUVAT?

SUVAT is a mnemonic for the five key variables in kinematic equations that describe motion with constant acceleration:

s

Displacement

u

Initial Velocity

v

Final Velocity

a

Acceleration

t

Time

These equations only apply when acceleration is constant. For varying acceleration, calculus-based methods are needed.

🧮 The Five SUVAT Equations

1.
v = u + ext{at}

Final velocity from initial velocity, acceleration, and time

(missing: s)
2.
s = ext{ut} + ½ ext{at}^{2}

Displacement from initial velocity, acceleration, and time

(missing: v)
3.
s = ext{vt} - ½ ext{at}^{2}

Displacement from final velocity, acceleration, and time

(missing: u)
4.
v^{2} = u^{2} + 2as

Final velocity from initial velocity, acceleration, and displacement

(missing: t)
5.
s = ½(u + v)t

Displacement from average velocity and time

(missing: a)

💡 How to Solve SUVAT Problems

Step-by-Step Method

  1. Identify what you know (at least 3 variables)
  2. Identify what you want to find
  3. Choose the equation that contains your known + unknown
  4. Substitute and solve
  5. Check with another equation if possible

Common Mistakes to Avoid

  • • Forgetting to use negative for deceleration
  • • Mixing up u (initial) and v (final)
  • • Using wrong units (always convert to SI)
  • • Applying to non-constant acceleration

❓ Frequently Asked Questions

What does SUVAT stand for?

SUVAT is a mnemonic for the five key variables in kinematic equations: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). These equations describe motion with constant acceleration.

When can I use SUVAT equations?

SUVAT equations only apply when acceleration is constant. For varying acceleration, calculus-based methods are needed. They work well for free fall, projectile motion (vertical component), and constant acceleration scenarios.

How many variables do I need to solve SUVAT?

You need at least 3 known variables to solve for the remaining 2 unknowns. Each SUVAT equation relates 4 variables, so with 3 known values, you can solve for the 4th, then use another equation to find the 5th variable.

What's the difference between u and v?

u is the initial velocity (velocity at time t=0), while v is the final velocity (velocity at time t). In equations like v = u + at, u represents the starting speed, and v represents the speed after acceleration a has acted for time t.

Can SUVAT handle negative acceleration?

Yes! Negative acceleration (deceleration) is simply acceleration in the opposite direction to velocity. For example, a car braking has negative acceleration. Just use the negative value for 'a' in the equations.

Why do I need to convert units to SI?

SUVAT equations work best with SI units (meters, m/s, m/s², seconds) because they're consistent. Mixing units (like feet and meters) leads to errors. Always convert all inputs to SI before calculating, then convert results back if needed.

What if acceleration isn't constant?

If acceleration varies with time, SUVAT equations don't apply. You'll need calculus: v = ∫a dt and s = ∫v dt. For position-dependent acceleration (like gravity at large distances), use energy methods or numerical integration.

📚 Official Data Sources

National Institute of Standards and Technology (NIST) ↗
SI units, physical constants, and measurement standards
Updated: 2026-01-15
MIT OpenCourseWare ↗
Physics course materials on kinematics and motion
Updated: 2026-01-10
Physics Hypertextbook ↗
SUVAT equations and kinematic formulas reference
Updated: 2025-12-20
Engineering Toolbox ↗
Kinematic equations and motion calculations
Updated: 2026-01-05

⚠️ Disclaimer: This calculator provides theoretical estimates based on SUVAT kinematic equations assuming constant acceleration. Actual motion may vary due to air resistance, friction, non-uniform gravitational fields, and other real-world factors. SUVAT equations are valid only for constant acceleration scenarios. For variable acceleration, projectile motion with air resistance, or relativistic speeds, more advanced methods are required. Always verify critical calculations with experimental measurements and professional engineering consultation. This calculator is for educational and preliminary design purposes only.

🔗 Related Calculators

🚀Velocity Calculator

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🍎Free Fall Calculator

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🎯Projectile Motion

Analyze projectile trajectories

📏Displacement Calculator

Calculate displacement

⚡Acceleration Calculator

Calculate acceleration

🎱Momentum Calculator

Calculate momentum

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

📐

v = u + at: velocity as function of time

— Kinematics

📏

s = ut + ½at²: displacement with constant a

— Kinematics

🚗

v² = u² + 2as: eliminates time from equations

— Kinematics

⚡

s = ½(u+v)t: uses average velocity

— Kinematics

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