Lab · Engineering Mechanics
Particle Motion Lab
A planar point particle under a constant acceleration or a constant resultant force. Every state is the exact closed-form solution at that instant, not a numerical integration.
Model
In the prescribed-acceleration mode no force model exists and none is invented. In the mass-and-forces mode the acceleration is ΣF/m, with gravity added only when it is switched on.
Inputs
Workspace
Clamped to 0 … 4 s.
The cursor reads the model at one instant. Slider and field are the same value. It changes nothing in the model and stays out of the shared link.
Trajectory
Framing only: the plotted coordinates are the same either way. “Include origin” keeps the global origin O and its axes in view, so the path is read against the frame the model is stated in.
Speed and velocity components
State at the cursor
| Time t | 0 s |
|---|---|
| Position r(t) | (0, 0) m |
| Displacement r(t) − r₀ | (0, 0) m |
| Velocity v(t) | (8, 0) m/s |
| Speed |v(t)| | 8 m/s |
| Acceleration a | (0, -2) m/s² |
| |a| | 2 m/s² |
Diagnostics
The model is complete and the trajectory is exact over the whole time window.
What this Lab models
A planar point particle under either a prescribed constant acceleration or a constant resultant force on a specified mass. Both modes give the exact closed-form trajectory and velocity history at any instant you choose, not a numerical simulation; the mass-and-forces mode additionally gives force, energy, momentum and impulse quantities.
Related calculations
Focused calculators
- Constant Acceleration
- Projectile Motion
- Circular Motion
- Curvilinear Motion
- Newton's Second Law
- Work–Energy
- Impulse–Momentum
- Collision
Each calculator solves one focused question with the same engine used here; the Circular Motion tool stays separate because a constant acceleration cannot represent circular motion.