Calculator Input
Choose the missing variable. Then enter the matching known values. The result appears above this form after submission.
Example Data Table
| Case | Initial Velocity | Acceleration | Time | Final Velocity | Displacement |
|---|---|---|---|---|---|
| Lift carriage start | 0 m/s | 1.5 m/s² | 8 s | 12 m/s | 48 m |
| Machine sled ramp-up | 4 m/s | 2.2 m/s² | 5 s | 15 m/s | 47.5 m |
| Conveyor slowdown | 10 m/s | -1 m/s² | 6 s | 4 m/s | 42 m |
| Track cart test | 3 m/s | 0.8 m/s² | 10 s | 11 m/s | 70 m |
| Press shuttle reverse | -2 m/s | 1.2 m/s² | 4 s | 2.8 m/s | 1.6 m |
Formula Used
Final velocity: v = u + at
Use this when initial velocity, acceleration, and time are known.
Acceleration: a = (v - u) / t
Use this when two velocities and elapsed time are known.
Time: t = (v - u) / a
Use this when velocity change and constant acceleration are known.
Displacement: s = ut + 0.5at²
This gives distance with direction under constant acceleration.
Average velocity: vavg = s / t = (u + v) / 2
This works for motion with constant acceleration over the interval.
How to Use This Calculator
- Select the variable you want to solve.
- Enter the known motion values in the form.
- Choose matching units for every entered quantity.
- Set decimal places and chart point count.
- Click Calculate Motion to generate the result.
- Review the summary table and motion graph.
- Use the export buttons to save CSV or PDF files.
FAQs
1. What does this calculator solve?
It solves one missing motion variable at a time. You can calculate final velocity, initial velocity, acceleration, time, or displacement using constant acceleration equations.
2. When should I use these formulas?
Use them for straight-line motion with constant acceleration. They fit many engineering checks, machine movements, lift studies, transport testing, and controlled motion simulations.
3. Can I enter negative values?
Yes. Negative values can represent reverse direction or deceleration. Keep the sign convention consistent across velocity, acceleration, and displacement to avoid misleading results.
4. Why must time stay above zero?
Time represents an elapsed interval in this model. Zero or negative time makes the physical interpretation unclear, so the calculator blocks those cases.
5. Does the graph update automatically?
Yes. After each calculation, the Plotly graph redraws using the computed motion interval. It plots velocity and displacement against time for quick visual review.
6. What units are supported?
You can work with m/s, km/h, ft/s, m/s², ft/s², g, seconds, minutes, hours, meters, kilometers, and feet. Internal conversion keeps the equations consistent.
7. What do the CSV and PDF exports contain?
They contain the latest result summary, including solved mode, velocities, acceleration, time, displacement, and average velocity. This helps with documentation and reporting.
8. Can I use this for non-constant acceleration?
No. The equations here assume constant acceleration during the whole interval. For varying acceleration, use calculus-based or simulation-based methods instead.