Kinematics Solver
Precision SUVAT Engine
Master the laws of motion. Solve for displacement, velocity, and acceleration with 100% algebraic accuracy using optimized SUVAT algorithms.
Variable Input
Solved Variables
Motion Output
Kinematics is the branch of classical mechanics that describes the motion of points, bodies, and systems of bodies. It relies on four fundamental variables: Time, Position, Velocity, and Acceleration.
The solver utilizes the SUVAT equations, a set of five kinematic formulas that connect these variables under the condition of constant acceleration. By providing any three known values, our high-authority algorithm can derive the remaining two instantly.
The Insider’s Guide to Motion Analysis
Solving kinematics is as much about Frame of Reference as it is about formulas. Most errors stem from inconsistent sign conventions.
1. The "Constant Acceleration" Trap
New students often try to apply SUVAT to objects like a rocket launch or a car changing gears. SUVAT only works if acceleration is constant.
Strategic Insight: If acceleration changes (non-uniform motion), you cannot use these formulas directly. You must use Calculus () or break the motion into separate "intervals" where acceleration is constant within each piece.
2. Master the Sign Convention
Velocity and acceleration are Vectors. If you decide that "Up" is positive, then gravity () must be entered as .
Pro Tip: Always draw a diagram and define your positive direction (+x, +y) before entering values into the solver. A negative sign in the result doesn't mean "error"—it simply means the object is moving in the direction opposite to your chosen positive.
The Big Five: SUVAT Equations
To solve any kinematic problem, we use the following equations derived from the definition of acceleration and velocity.
Velocity-Time
Displacement-Time
Time-Independent
Average Velocity
Alternative Displacement
Variables: s = Displacement, u = Initial Velocity, v = Final Velocity, a = Constant Acceleration, t = Time.
| Scenario | Knowns | Key Formula |
|---|---|---|
| Coming to a Stop | ||
| Free Fall Drop | ||
| Constant Cruise |
संबंधित उपकरण
Distance vs. Displacement: What's the difference?
Distance is scalar (how far you traveled total). Displacement is a vector (the straight-line distance from Start to Finish). If you run around a 400m track and end where you started, your distance is 400m, but your displacement is zero.
Can acceleration be negative if an object is speed up?
Yes! If your positive direction is "Left" and the object is moving left and speeding up, both velocity and acceleration are negative. Acceleration is "negative" when it acts in the direction you defined as negative.
What does $v^2$ being positive imply?
Since any number squared is positive, the formula doesn't tell you the direction of final velocity. You must use logic to decide if the final object is moving in the positive or negative direction when taking the square root.
Is air resistance included?
Like most kinematic models, we assume a vacuum. Real-world motion involves air drag which increases with velocity squared, making acceleration non-constant.
Scalar
A quantity having only magnitude, not direction (e.g., mass, time, temperature).
Vector
A quantity having both magnitude and direction (e.g., velocity, force, displacement).
Instantaneous Velocity
The velocity of an object at a specific point in time, mathematically the derivative of position.
Reference Frame
A set of coordinates used to determine the position and velocities of objects in that frame.
Fact-Checked by the CalculatorsCentral Physics Lab. Numerical SUVAT solvers tested against NIST accuracy standards.
Last Updated: January 2026