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movement.md

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Movement

Units

  • $s =$ Distance
    • $[s] = m$
    • For the distance the symbols $x$, $sx$ or $h$ are also used.
  • $\Delta s =$ Distance difference
    • $[\Delta s]$ = m
    • $s_A$ = Start position | $s_E$ = End position
    • $\Delta s = s_E - s_A$
  • $t = $ Time
    • $[t] = s$ (seconds)
  • $\Delta t$ = Time interval
    • $[\Delta t]$ = s
    • $t_A$ = Start time | $t_E$ = End time
    • $\Delta t = t_E - t_A$
  • $v$ = Speed
    • $\displaystyle v [\frac{m}{s}] = \frac{\Delta s[m]}{\Delta t[s]} = \frac{s_E[m] - s_A[m]}{t_E[s] - t_A[s]}$
    • $[v]$ = m/s
    • $s_A$ = Initial position | $s_E$ = End position

It is an average speed in the time interval $\Delta t$. The smaller the measured time interval, the closer we get to an instantaneous speed.

  • $a$ = Acceleration
    • $\displaystyle a [\frac{m}{s^2}] = \frac{\Delta v[m/s]}{\Delta t[s]} = \frac{v_E[m/s] - v_A[m/s]}{t_E[s] - t_A[s]} \space \ \ \ \space [a] = m/s^2$
    • $v_A$= Initial speed $v_E$ = Final speed

It is an average acceleration in the time interval $\Delta t$. The smaller the measured time interval, the closer we get to an instantaneous acceleration.

Kinematics

Kinematics deals with the motion of point masses in space and time. We distinguish between straight-line movements in 1-dimensional space, 2-dimensional movements in a plane (surface), and 3-dimensional movements in space.

For each movement, a reference system (laboratory) must be defined in advance. For a straight-line movement (1-dimensional movement), the reference system is clearly defined by the origin (0), an axis (for example s, x, sx, h etc.), a direction (+), and a scaling of the axis:

The origin, direction, and scaling can be chosen so that a task can be solved simply. The scaling does not have to be explicitly specified. Only in drawn diagrams must the scale be recognizable in the representation.

For 2-dimensional movements, two perpendicular axes (e.g., x and y) and an origin are to be defined.

In order to start with kinematics, the quantities to be described such as distance, time, speed, and acceleration must be clearly defined. Here are the corresponding definitions: