Kinematics (SUVAT) Calculator
Enter exactly three known variables to calculate the remaining two using the equations of motion.
SUVAT Variables
Fill in exactly 3 text boxes and leave 2 empty
Calculation Results
Step-by-step SUVAT derivations
Provide at least 3 knowns to compute the remaining missing kinematic variables.
Kinematics (SUVAT) Calculator: Master Equations of Motion
Welcome to the Kinematics (SUVAT) Calculator, your essential tool for solving 1D constant acceleration problems. Whether you are a physics student analyzing moving objects, an engineer calculating braking distances, or simply exploring the laws of classical mechanics, this calculator uses the four standard equations of motion to automatically resolve any missing variables. By providing exactly three known parameters (Displacement, Initial Velocity, Final Velocity, Acceleration, or Time), the solver dynamically routes the information through the fundamental kinematic formulas to instantly derive the remaining two variables.
Key SUVAT Formulas
The Four Equations of Motion
1. Velocity-Time: v = u + at
2. Displacement-Time: s = ut + ½at²
3. Velocity-Displacement: v² = u² + 2as
4. Average Velocity: s = ½(u + v)t
These equations assume that acceleration remains constant and motion occurs in a straight, 1-dimensional line. Each formula intentionally excludes one of the five variables, allowing our engine to cross-reference and isolate unknowns efficiently.
How to Use the Kinematics Calculator
- Identify Knowns: Read your physics problem and identify the three variables you already have quantitative values for.
- Input Values: Enter these exactly into the corresponding fields: s (m), u (m/s), v (m/s), a (m/s²), or t (s).
- Leave Unknowns Blank: Leave exactly two text fields completely empty. The calculator will target these.
- Solve: Click the 'Solve Equations' button to initiate the kinematic routing engine.
- Review Steps: The result pane will not only display the final numerical values of your missing variables, but also the algebraic derivation steps taken to reach them.
Features of this Solver
- ✓Multi-dimensional Routing: Automatically determines the correct formula sequence based on your blanks.
- ✓Algebraic Explanations: Displays human-readable logic flows showing exactly how formulas were isolated.
- ✓Quadratic Handling: Successfully traverses the quadratic equation when finding time (t) from a displacement function.
- ✓Sign Awareness: Computes completely accurately with negative velocities or negative acceleration (deceleration).
Example Problem: Braking Car
Scenario: Calculating Stopping Distance
A car is travelling at 25 m/s (u). The driver hits the brakes, causing a deceleration of -5 m/s² (a). We want to find the total distance travelled (s) before coming to a complete stop (v = 0).
Known Inputs: Initial Velocity (u) = 25, Final Velocity (v) = 0, Acceleration (a) = -5
Engine Process:
- The engine recognizes we have (u, v, a) and are looking for 's'.
- It selects the formula: v² = u² + 2as
- It isolates for s: s = (v² - u²) / (2a)
- s = (0² - 25²) / (2 * -5) = -625 / -10 = 62.5 meters.
Result: The car stops after traveling exactly 62.5 meters.
Academic & Scientific References
For further understanding and validation of the formulas used above, we recommend exploring these authoritative resources: