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Acceleration is the rate of change of velocity — how quickly an object speeds up, slows down, or changes direction. It is a vector quantity with both magnitude and direction. An object accelerates whenever its velocity changes, whether that change is in speed, direction, or both.
There are two key formulas for acceleration: the kinematic formula a = (v − u)/t (change in velocity divided by time), and Newton's second law a = F/m (net force divided by mass). The kinematic form is used when you know the initial and final velocities and time; the dynamic form is used when you know the forces acting on the object.
The SI unit of acceleration is metres per second squared (m/s²). The acceleration due to gravity near Earth's surface is g = 9.81 m/s² downward, often approximated as 10 m/s². A fighter pilot experiencing 9g acceleration feels nine times their body weight — modern aircraft rarely exceed 9g, which is near the human tolerance limit.
Worked example: A cyclist decelerates from 12 m/s to 4 m/s in 4 seconds. Acceleration a = (4 − 12)/4 = −8/4 = −2 m/s². The negative sign indicates deceleration (acceleration opposite to the direction of motion).
a = (v − u) / t | a = F / m
a = (v − u) / t
Acceleration Formulas
| Formula | Description | Units |
|---|---|---|
| a = (v − u) / t | Change in velocity over time | m/s² |
| a = F / m | Newton's 2nd Law | m/s² |
| a = Δv / Δt | Instantaneous acceleration | m/s² |
| g = 9.81 m/s² | Gravitational acceleration (Earth) | m/s² |
| g = 1.62 m/s² | Gravitational acceleration (Moon) | m/s² |
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.