Calculator Inputs
Enter any compatible known values. Select the variable to solve. Leave the target field blank or let it be overwritten.
Example data table
| Scenario | u (m/s) | a (m/s²) | t (s) | v (m/s) | s (m) |
|---|---|---|---|---|---|
| Car speeding up uniformly | 5 | 2 | 4 | 13 | 36 |
| Train slowing down | 30 | -1.5 | 8 | 18 | 192 |
| Lift rising steadily faster | 1 | 0.8 | 6 | 5.8 | 20.4 |
Formula used
Velocity relation
v = u + at
Displacement from start data
s = ut + (1/2)at²
Displacement from end data
s = vt - (1/2)at²
Average velocity form
s = ((u + v) / 2)t
No-time relation
v² = u² + 2as
Average velocity
v̄ = (u + v) / 2
These equations apply when acceleration stays constant throughout the motion interval.
How to use this calculator
- Select the variable you want to solve.
- Enter at least three compatible known values.
- Choose the correct unit beside every input.
- Set decimal places and graph sample count.
- Press Calculate Motion to view the result above the form.
- Review the solved table, notes, and graph.
- Use the CSV or PDF buttons to export your report.
Frequently asked questions
1. What does uniform acceleration mean?
Uniform acceleration means acceleration stays constant over time. Velocity changes by equal amounts during equal time intervals, which makes the standard motion equations valid.
2. How many values do I need?
You usually need three compatible known values to solve the fourth motion quantity. The calculator checks combinations and applies a suitable constant-acceleration equation automatically.
3. Can I enter negative acceleration?
Yes. Negative acceleration is allowed and often represents deceleration or motion opposite the chosen positive direction. Negative displacement and velocity can also be used.
4. Why can time have two answers?
Quadratic motion equations can produce two non-negative times. That happens when the same displacement can occur at two moments. This calculator reports the smaller valid root and notes the alternative.
5. Why can square-root formulas be ambiguous?
Equations involving squared velocity return a magnitude, not a guaranteed direction. The calculator chooses a direction matching the current motion trend and tells you when another sign is possible.
6. Which units are supported?
Velocity supports m/s, km/h, and ft/s. Acceleration supports m/s², ft/s², and g. Time supports seconds, minutes, and hours. Displacement supports meters, kilometers, and feet.
7. What does the graph show?
The graph plots displacement, velocity, and acceleration across the solved time range. It helps you see how position curves, velocity changes linearly, and acceleration remains constant.
8. Are the exports useful for class or lab work?
Yes. The CSV export is useful for spreadsheets and record keeping. The PDF export captures the visible result section, making it practical for notes, assignments, or reports.