Calculator · Engineering Mechanics
Constant Acceleration Calculator
Exact constant-acceleration kinematics of a point particle: v = v₀ + a·t and r = r₀ + v₀·t + ½·a·t², solved analytically rather than integrated.
Problem
Known values
Each mode uses exactly one relation. Nothing is inferred from a contradictory mix of values — pick the set you actually know.
Results
| Relation used | v = v₀ + a·t and Δx = v₀·t + ½·a·t² |
|---|---|
| Initial velocity v₀ | 2 m/s |
| Velocity v | 14 m/s |
| Acceleration a | 3 m/s² |
| Time t | 4 s |
| Displacement Δx | 32 m |
| Average velocity (v₀ + v)/2 | 8 m/s |
Technical reference
v = v₀ + a·t
Δx = v₀·t + ½·a·t²
- v₀
- initial velocity[m/s]
- v
- velocity at time t[m/s]
- a
- constant acceleration[m/s²]
- Δx
- displacement[m]
- t
- elapsed time[s]
Every relation here assumes a strictly constant acceleration over the interval; only the relation matching the selected solve mode is used, so an over-determined or contradictory input set is never silently reconciled.
Assumptions
- · Point particle: no size, no orientation and no rotation.
- · The acceleration is constant over the whole interval.
- · Results are the exact closed-form solution, not a numerical integration.
- · Time runs forward from the stated initial state; t ≥ 0.
Continue
Open in Particle Motion Lab
The same initial state and acceleration, with a trajectory and a time cursor.