Kinematics is a branch of physics studies with the motion of a body or bodies without consideration of the forces involved.

### Motion with constant velocity

Constant velocity means that the velocity does not change in the time period we are looking at. This is also referred to as a uniform velocity. The velocity and time can be recorded over time:

The Greek letter ∆ (spocken "delta") stands for `difference`. The difference of the distance ∆s can also be negative, i.e. Δs < 0. In our example, this would be the case if the car is moving backwards.

The greater the speed, the steeper the course of the straight line in the s(t)-graph.

The value that the function s(t) takes at a given time t corresponds to the area between the v(t) characteristic and the t-axis. Thus, the distance traveled is calculated: **s(t) = v × t**

### Multidimensional motions with constant velocity

The rules for one-dimensional motions can be applied to two- or three-dimensional motions. The velocity can be divided into the single components (x-, y- and z). The analysis of the individual components is needed, for example, for the addition of velocities. We will take a closer look at three-dimensional motion:

### Adding velocities

If two motions are rectilinear in the same direction, the resulting velocity can be obtained by simply adding the two velocity amounts v_{1} and v_{2}.

Example treadmill in the airport: A person moves with a speed v1 on a treadmill within the airport with the treadmill speed v_{2}. The amounts of both speeds add up. The resulting speed v of the person (relative to the ground) is thus **v _{tot} = v_{1} + v_{2}.**

If the velocities are at any angle to each other, the resulting velocity is determined by vector addition - either graphically or mathematically.

Example: A boat crosses a river vertically at a speed v_{1} = 3 m/s; the flow velocity of the river is v_{2} = 1 m/s.

Our example corresponds to a two-dimensional motion, i.e. motion in a plane. The motion divided into x- and y-component results in:

The value of the resulting velocity can be determined via Pythagoras:

The angle of the resulting velocity can be determined by an angular function. We choose the tangent:

Back to our example: