Kinematic Equations Solver

The SUVAT equations are a set of five fundamental equations in classical mechanics that describe the motion of an object under constant acceleration. They relate s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). These equations are essential for solving problems in physics and engineering involving linear motion.

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 compatible units.

These errors occur when the kinematic equations produce a negative discriminant (e.g., under a square root) or a negative time value. This typically means your input values describe a physically impossible scenario, such as:

• 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.

No. The SUVAT equations require exactly four known variables to solve for the fifth. You must mark only one variable as unknown at any time. If you need to solve for multiple variables, run the solver multiple times, each time marking a different variable as unknown.

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): The object is decelerating (slowing down) in the direction of motion. However, time (t) should always be positive. If you get a negative time, it may indicate an error in your inputs or assumptions.

The solver uses floating-point arithmetic and provides results with up to 8 decimal places of precision. You can adjust the displayed precision using the Precision dropdown. For most physics and engineering applications, 4 decimal places are sufficient.

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 motion is at constant velocity. The equations simplify as follows:

• 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 these special cases automatically.

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.