# Physics with Calculus/Mechanics/Linear Motion and Statics

How fast is an object moving in a particular direction? Where will this object be at any time on that one dimensional line (the direction in question)? Linear motion addresses this question.

Linear motion deals with the motion or change in position of on object on a line (or in one dimension). Thus we can represent an objects position with respect to a point on that line with one value.

## An Object's Location[edit]

If an object is at rest it is, by definition, not changing position. In this case we can only talk about where this object is in relation to some point. Since we are merely talking about linear space (that is motion on a line), we can represent this distance or displacement with the value of x. Let us also use the international units of meters.

If we pick a particular point on a line as the relational point and then place an object directly on that point we can say that that object is at 0 meters, or x=0m. Let's say this line is a horizontal line and we make the right side of this line be the positive direction and the left side of this line be the negative direction. If we take this object and move it 1 meter to the right (the positive direction), we can say that the object is at 1 meters, or x=1m. We can also say that the object change in position (delta x) is 1 meter (1 meter - 0 meter = 1 meter).

**delta** means the change in, or the final value minus the initial value.

**delta x** means the change in x, or the x(final) - x(initial)

If we take this same object and move it to the left 2 meters we will have

**delta x** = (-1 meter) - (1 meter)

or

**delta x** = -2 meters

## An Object's Velocity[edit]

Notice, this object is moving. That is, it is changing it's position. Average **Velocity** is a measurement of the change in position of an object in a particular direction with respect to the change in time during which the object moved. For instance, if an objects change in position, that is delta x, is +2 meters during a 2 second time frame, then the average velocity is 2 meter for every 2 second, or 2m/ 2s, or 1m/ 1s.

**velocity** is the motion of an object in a particular direction and is what is called a vector.