<p align="right">Last Update: <font color="#4f81bd">November 12, 2024</font></p>
## BIG IDEAS
- Acceleration ( $\vec{a}$ ) is the change in [[Velocity|velocity]] over the change in [[Time|time]].
- Another way of stating this is that acceleration is the rate of change in velocity with respect to time.
- It is a [[Vectors|vector]] quantity.
- $\vec{a}$ is the symbol for acceleration.
- The [[SI units]] are meters per second per second (m/s<sup>2</sup>).
- Sometimes the units are written m/s/s.
>[!important]
>An object whose velocity is changing is accelerating. This means a change in speed or direction.
### Formula
$\vec{a} \ = \ \frac{\Delta v}{\Delta t} \ = \ \frac{v - v_0}{t} \tag{1}$
where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time.
#### Kinematic Equation 1: Rearrange Definition
$v = a \cdot t + v_0 \tag{2}$
### Types of Acceleration
- Linear acceleration
- Instantaneous acceleration
- Uniform acceleration (constant acceleration)
- Gravitational acceleration (acceleration due to gravity)
- Centripetal acceleration (also known as radial acceleration)
- Tangential acceleration
- Angular acceleration
- Translational acceleration
>[!attention] Clarification
><font color="#f79646">Speeding up</font>
When acceleration and the direction of motion are the same
>- If acceleration is positive and velocity is positive
>- if acceleration is negative and velocity is negative
>
><font color="#f79646">Slowing down</font>
>When acceleration and the direction of motion are opposite.
>- if acceleration is positive and velocity is negative
>- if acceleration is negative and velocity is positive
### Relationship to forces
Acceleration is directly related to the net force acting on an object and inversely related to its mass (Newton's Second Law of Motion).
$a \ = \ \frac{\Sigma F}{m} \tag{3}$
where $\Sigma F$ is the net force acting on the object, $m$ is the mass of the object, and $a$ is the acceleration.
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