KEVOS® MAKEOS · Mechanics
Uniformly Accelerated Motion and Falling Bodies
How fast and how far does this body travel under constant acceleration, or how fast does it hit the ground?
Final velocity and distance from initial velocity, acceleration and time; the acceleration and time needed to change speed over a distance; and the impact speed and time of a body falling from a height.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known values | choice | Choose which values you know. |
| Initial velocity | m/s | Velocity at the start (downward for a fall). |
| Acceleration (negative to decelerate) | m/s² | Constant acceleration; enter a negative value for braking. |
| Time | s | Duration of the acceleration. |
| Final velocity (distance mode) | m/s | Velocity at the end of the distance. |
| Distance (distance mode) | m | Distance over which the speed changes. |
| Fall height (fall mode) | m | Height of the fall. |
Method and formulas
- v = u + a t and s = u t + ½ a t².
- a = (v² − u²) ÷ 2 s and t = 2 s ÷ (u + v).
- Falling body: v = √(u² + 2 g h), t = (v − u) ÷ g, with g = 9.80665 m/s².
- Example: from rest at 2 m/s² for 5 s a body reaches 10 m/s after 25 m.
Limitations
- Constant acceleration only; real drives ramp acceleration (jerk limits).
- Air resistance is neglected for falling bodies.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a conveyor or slide acceleration ramp
- Check stopping distance for a decelerating carriage
- Estimate the impact speed of a dropped part
Who it is for
- Design engineers
- Mechanical engineers
- Engineering students
What you get
- Final velocity
- Distance travelled or acceleration needed
- Time taken
Interpreting the result
- For a fall the impact energy is m g h; use it with an impact or shock-load tool to size the stop.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 175–181. Topic reference; no source tables or recommended settings are reproduced.
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