Kinematic Equations Solver

The SUVAT equations relate s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time) for linear motion with constant acceleration.

You can use any consistent set of units, but the most common are:

• Displacement (s): meters (m)
• Velocity (u, v): meters per second (m/s)
• Acceleration (a): meters per second squared (m/s²)
• Time (t): seconds (s) The solver does not convert units, so ensure all your inputs use a compatible system.

These errors can occur when a selected equation has no real solution for the inputs or the solver finds no non-negative time. They can indicate incompatible values or a combination the solver does not support. Check the values, signs, units, and assumptions.

• An object accelerating in the opposite direction of its motion but still increasing speed.
• A displacement that cannot be achieved with the given acceleration and time.
• A final velocity that is less than the initial velocity with positive acceleration. Double-check your inputs for consistency.

Mark one variable as unknown and enter the other four. The solver then uses a supported equation combination; it does not guarantee a solution for every set of values.

Negative values can be physically meaningful in kinematics:

• Negative displacement (s): The object is moving in the opposite direction of your defined coordinate system.
• Negative velocity (u, v): The object is moving in the opposite direction of your coordinate system.
• Negative acceleration (a): Acceleration points in the negative direction of your coordinate system; whether the object speeds up or slows down depends on its velocity. The solver looks for a non-negative time solution. A negative-time mathematical result may describe motion before the chosen reference time rather than a future elapsed time.

The solver uses floating-point arithmetic. The Precision control changes how many decimal places are displayed; it does not guarantee physical accuracy or replace appropriate significant figures.

Yes, but with some considerations:

• Vertical motion: Use a = 9.81 m/s² (gravity) or a = -9.81 m/s² (if your coordinate system defines upward as positive).
• Horizontal motion (no air resistance): Use a = 0.
• 2D projectile motion: Solve the horizontal (x) and vertical (y) components separately, as they are independent of each other.

If acceleration (a = 0), the equations reduce to constant-velocity motion. For example:

• v = u (final velocity equals initial velocity)
• s = ut (displacement equals initial velocity multiplied by time)
• t = s/u (time equals displacement divided by initial velocity, if u ≠ 0) The solver handles some zero-acceleration cases when the selected inputs are supported.

No. This solver is designed for linear motion with constant acceleration (SUVAT equations). For circular or rotational motion, you would need to use angular kinematic equations, which involve angular displacement, angular velocity, angular acceleration, and torque. These are not supported by this tool.

Always consider the context of your problem:

• Sign: Positive/negative values indicate direction relative to your coordinate system.
• Magnitude: Ensure the values are realistic for your scenario (e.g., a car’s acceleration of 100 m/s² is unrealistic).
• Units: Double-check that your inputs and outputs use consistent units.