Acceleration
Acceleration is the rate at which velocity changes, found by dividing the change in velocity by the time it takes.
Formula
a = \frac{\Delta v}{\Delta t}
Definition
Acceleration is how quickly something speeds up, slows down, or changes direction; any change in motion counts. Quantitatively it is the rate of change of velocity, $a = \Delta v / \Delta t$, with SI unit meters per second squared ($\text{m/s}^2$). Acceleration in the direction of motion speeds an object up, acceleration opposite the motion slows it down, and near Earth's surface falling objects accelerate at $g = 9.8\ \text{m/s}^2$. As a vector, $\vec{a} = d\vec{v}/dt = d^2\vec{r}/dt^2$ can point in any direction relative to $\vec{v}$: parallel components change speed, while perpendicular components change direction, giving centripetal acceleration $a_c = v^2/r$. By Newton's second law, $\vec{a} = \vec{F}_{\text{net}}/m$, so acceleration always points along the net force.
Example
A skateboard rolling faster and faster down a hill is accelerating, and when the rider drags a foot to slow down, that is acceleration too, just in the opposite direction. A car that goes from $0$ to $24\ \text{m/s}$ in $8\ \text{s}$ has an acceleration of $24 \div 8 = 3\ \text{m/s}^2$, meaning its velocity grows by $3\ \text{m/s}$ every second. For a vertical case, a ball thrown straight up at $19.6\ \text{m/s}$ with $a = -9.8\ \text{m/s}^2$ reaches the top when $v = 0$, at $t = 19.6/9.8 = 2\ \text{s}$, and rises $h = v_0 t + \tfrac{1}{2}at^2 = 39.2 - 19.6 = 19.6\ \text{m}$.
Key Insight
In everyday talk, "accelerate" means speed up, but in physics slowing down and turning are also acceleration because velocity is changing. On a velocity-versus-time graph, acceleration is the slope, so a horizontal line means constant velocity and zero acceleration even if the object is moving fast. The thrown ball makes the point sharply. At the very top of its flight it has zero velocity but still accelerates at $9.8\ \text{m/s}^2$ downward; zero velocity does not mean zero acceleration, because gravity never pauses.