Velocity

Velocity tells us how an object's position changes over time. It answers two important questions: How fast is something moving? And which direction is it going?

Visualizing Motion

Let's see how velocity works with a moving object:

In this example, the object starts at $x_0 = 2$ meters, it moves right by $\Delta x = 8$ meters, and it takes $\Delta t = 2$ seconds. The velocity of the object is given by:

$\vec{v} = \dfrac{\Delta x}{\Delta t} = \dfrac{8\text{ m}}{2\text{ s}} = 4$ m/s in the positive direction.

Note: In 1D, like for displacement, we may sometimes drop the "direction", as well as the arrows above $v$ and $\Delta x$, since the direction should be clear from whether it is a positive or negative value, so long as we've labelled our coordinate system appropriately.

Direction Matters

Velocity is a vector – it has both size and direction. The sign tells us which way the object is moving:

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