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:
If two motions are rectilinear in the same direction, the resulting velocity can be obtained by simply adding the two velocity amounts v1 and v2.
Example treadmill in the airport: A person moves with a speed v1 on a treadmill within the airport with the treadmill speed v2. The amounts of both speeds add up. The resulting speed v of the person (relative to the ground) is thus vtot = v1 + v2.
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 v1 = 3 m/s; the flow velocity of the river is v2 = 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:
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