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.
Why This Physics Calculation Matters
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 equivalentโany three variables determine the system.
- โv = u + at (no displacement)
- โs = ut + ยฝatยฒ (no final velocity)
- โvยฒ = uยฒ + 2as (no time)
- โs = ยฝ(u+v)t (no acceleration)
๐ Sample Motion Scenarios
Click an example to load predefined values:
๐ The Five SUVAT Equations
Final velocity from initial velocity, acceleration, and time
Displacement from initial velocity, acceleration, and time
Displacement from final velocity, acceleration, and time
Final velocity from initial velocity, acceleration, and displacement
Displacement from average velocity and time
โ๏ธ SUVAT Variables
Instructions: Select exactly 3 known variables (highlighted in blue). The calculator will solve for the other 2.
Displacement
Initial Velocity
Final Velocity
Acceleration
Time
โ Complete SUVAT Solution
Equations Applied:
๐ Motion Visualization
๐ Position vs Time
s = ut + ยฝatยฒ visualization
๐ Velocity vs Time
v = u + at (linear relationship)
๐ SUVAT Values Comparison
โก Kinetic Energy (per kg)
๐ Step-by-Step Solution
Initial Velocity (u): 0.00 m/s
Final Velocity (v): 20.00 m/s
Acceleration (a): 2.00 m/sยฒ
Using t = (v - u) / a
t = (20.00 - 0.00) / 2.00
โ t = 10.0000 s
Using s = ut + ยฝatยฒ
s = (0.00 ร 10.00) + (0.5 ร 2.00 ร 10.00ยฒ)
โ s = 100.0000 m
Average Velocity: v_avg = (u + v) / 2
โ v_avg = 10.0000 m/s
Velocity Change: ฮv = v - u
โ ฮv = 20.0000 m/s
Motion Type: Accelerating
๐ What is SUVAT?
SUVAT is a mnemonic for the five key variables in kinematic equations that describe motion with constant acceleration:
Displacement
Initial Velocity
Final Velocity
Acceleration
Time
These equations only apply when acceleration is constant. For varying acceleration, calculus-based methods are needed.
๐งฎ The Five SUVAT Equations
Final velocity from initial velocity, acceleration, and time
(missing: s)Displacement from initial velocity, acceleration, and time
(missing: v)Displacement from final velocity, acceleration, and time
(missing: u)Final velocity from initial velocity, acceleration, and displacement
(missing: t)Displacement from average velocity and time
(missing: a)๐ก How to Solve SUVAT Problems
Step-by-Step Method
- Identify what you know (at least 3 variables)
- Identify what you want to find
- Choose the equation that contains your known + unknown
- Substitute and solve
- Check with another equation if possible
Common Mistakes to Avoid
- โข Forgetting to use negative for deceleration
- โข Mixing up u (initial) and v (final)
- โข Using wrong units (always convert to SI)
- โข Applying to non-constant acceleration
โ 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/sยฒ, 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 = โซa dt and s = โซv dt. For position-dependent acceleration (like gravity at large distances), use energy methods or numerical integration.
๐ Official Data Sources
โ ๏ธ 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.
๐ Related Calculators
โ ๏ธFor educational and informational purposes only. Verify with a qualified professional.
๐ฌ Physics Facts
v = u + at: velocity as function of time
โ Kinematics
s = ut + ยฝatยฒ: displacement with constant a
โ Kinematics
vยฒ = uยฒ + 2as: eliminates time from equations
โ Kinematics
s = ยฝ(u+v)t: uses average velocity
โ Kinematics