Description
Return signed midpoint/average velocity and displacement under one constant-acceleration interval.
A mechanics calculation needs a coordinate frame, sign convention, and consistent force, length, mass, and time units. Vector projections, local balance terms, and ideal motion equations describe particular parts of a physical model. They do not automatically establish all equilibrium conditions or the validity of the model.
Return signed midpoint/average velocity and displacement under one constant-acceleration interval.
When to use this tool
Use Constant Acceleration Midpoint Speed when you need this particular projection, balance, frame conversion, or ideal-model component from supplied physical quantities.
How to use the tool and how it works
- Enter initialVelocity, acceleration, duration. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read midpointVelocity, averageVelocity, displacement. Use the output convention below.
For nonnegative duration return midpointVelocity=initialVelocity+acceleration*duration/2, averageVelocity equal to that value, and displacement=midpointVelocity*duration.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initialVelocity | Initial Velocity | Required. Finite number. |
| acceleration | Acceleration | Required. Finite number. |
| duration | Duration | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| midpointVelocity | Signed velocity at half the supplied duration; not speed magnitude. | Required. Finite number. |
| averageVelocity | Average Velocity | Required. Finite number. |
| displacement | Signed displacement in the stated length unit, or vector components where declared. | Required. Finite number. |
{
"input": {
"initialVelocity": 2,
"acceleration": 3,
"duration": 4
},
"output": {
"midpointVelocity": 8,
"averageVelocity": 8,
"displacement": 32
}
}Limitations and assumptions
- Velocity and acceleration are signed along one axis and use compatible units. Despite the tool name, outputs are velocities rather than speed magnitudes; equality of midpoint and average assumes constant acceleration.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete force, motion, or energy model when a single contribution is insufficient. Check coordinate frames, idealizations, and dimensional consistency before combining calculated terms.
References
Similar or alternative tools
- Acceleration Tangent Normal Orthogonality
Check a supplied tangent/normal acceleration decomposition using an explicit absolute dot-product tolerance.
- Physics: Collision Restitution Relative Speed
Apply the normal coefficient-of-restitution relation to a nonnegative approach speed under an explicitly passive 0..1 restitution model; not a collision impulse solver.