The Definition of Acceleration
In physics, acceleration is defined as the rate at which an object changes its velocity. It is a measure of how quickly an object is speeding up, slowing down, or changing direction.
Because velocity is a vector (meaning it has both speed and direction), acceleration is also a vector. This means you can experience physical acceleration without ever pressing the gas pedal:
- Speeding Up: Driving a car from $0$ to $60 , \text{mph}$ (changing magnitude).
- Slowing Down: Slamming on the brakes to stop at a red light (changing magnitude, technically known as deceleration or negative acceleration).
- Turning: Driving at a perfectly steady $30 , \text{mph}$ around a sharp curve (changing direction).
Calculating Constant Acceleration
This calculator determines the average uniform acceleration of an object over a specific time period. To calculate this, you only need three variables: the velocity you started at, the velocity you ended at, and how long the change took.
The Formula
The formula for average acceleration ($a$) is the change in velocity ($\Delta v$) divided by the change in time ($\Delta t$).
Example Calculation
Imagine a sports car accelerates from a standstill ($0 , \text{m/s}$) to a final velocity of $27 , \text{m/s}$ (roughly $60 , \text{mph}$) in exactly 4.5 seconds.
- Change in Velocity: $27 , \text{m/s} - 0 , \text{m/s} = 27 , \text{m/s}$
- Calculation: $a = \frac{27}{4.5} = \mathbf{6.0 , \text{m/s}^2}$
This means that for every second the driver has their foot on the gas, the car's speed increases by $6.0 , \text{meters per second}$.
Understanding the Units (m/s²)
The SI unit for acceleration is meters per second squared ($m/s^2$). While this unit can look confusing, it simply means "meters per second, per second." It tells you how many meters per second of speed you gain every single second.
If you drop an object off a building, Earth's gravity accelerates it at $9.8 , \text{m/s}^2$.
- After 1 second, it is falling at $9.8 , \text{m/s}$.
- After 2 seconds, it is falling at $19.6 , \text{m/s}$.