Kinematic Equations Calculator
Enter three known values (initial velocity, final velocity, acceleration, time, or displacement) to solve for the remaining two unknowns in one-dimensional motion.
Enter Three Known Variables
Calculation Results
Input exactly three known variables (Initial Velocity, Final Velocity, Acceleration, Time, or Displacement) to solve the system.
Important Info: The Kinematic Equations (SUVAT)
Kinematics is the branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies without considering the forces that cause them to move. This calculator uses the four standard kinematic equations, often referred to as the **SUVAT** equations, which only apply to motion with **constant acceleration** in one dimension.
Understanding the Variables:
The five primary variables used in these equations are: [Image of kinematic variables in constant acceleration]
- $v_i$ (or $u$): Initial Velocity
- $v_f$ (or $v$): Final Velocity
- $a$: Acceleration (must be constant)
- $\Delta t$ (or $t$): Time interval
- $\Delta x$ (or $s$): Displacement (change in position)
The Four Fundamental Equations:
Why Use This Kinematic Calculator?
Solving kinematic problems by hand can be time-consuming and prone to algebraic errors, especially when isolating a variable that's squared. This tool automates the process, allowing engineers, physicists, and students to quickly verify results and focus on conceptual understanding. Key applications include:
- **Projectile Motion:** Analyzing the vertical or horizontal components of objects thrown or launched.
- **Vehicle Dynamics:** Calculating stopping distance, required acceleration, or final speed of cars, trains, or rockets.
- **Free Fall:** Determining the time it takes for an object to fall a certain distance under the influence of gravity ($a = 9.8 \text{ m/s}^2$ or $32.2 \text{ ft/s}^2$).
- **Academic Study:** Checking homework problems and understanding the relationship between the five variables.
How to Use the Solver
- Identify Knowns and Unknowns: Read your physics problem and list the values for the five variables ($v_i, v_f, a, \Delta t, \Delta x$).
- Ensure Consistent Units: All your input values must use a single, consistent unit system (e.g., all SI units: meters, seconds, $m/s$, $m/s^2$).
- Input Three Values: Enter the known values into the corresponding input fields. The calculator requires **exactly three** known values to solve for the remaining two.
- Solve: Click the "Solve for Unknowns" button. The tool will select the appropriate kinematic equation (the one that excludes one of the known variables) and rearrange it to find the two missing values.
Frequently Asked Questions (FAQ)
What happens if I enter four or more values?
This calculator is designed to solve a system of equations, which requires three inputs to find the two unknowns. If you enter four or more values, the tool will warn you, as the extra inputs are mathematically redundant or may contradict the results from the three primary inputs.
Can I use this for non-constant acceleration?
No. The core assumption of all four kinematic equations is that acceleration ($a$) is constant throughout the motion. If acceleration is changing, you must use calculus (integration) or numerical methods to solve the problem.
Does this tool handle unit conversions or currency?
This tool performs only the mathematical calculations (e.g., division, multiplication, square roots). It does not handle unit conversions (like miles/hour to meters/second) or currency, as those are irrelevant to physics calculations. Please ensure your inputs are in a single, consistent unit system before calculating.