17 lines
568 B
Markdown
17 lines
568 B
Markdown
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# Gleichmässig Beschläunigte Bewegung
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Bewegung mit konstanter Beschläunigung
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$$a = const.$$
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$$v(t) = v(0) + a * t$$
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$$a = \frac{\Delta v}{\Delta t}$$
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$$\int^{v(t)}_{v(0)} \Delta v = \int^t_0 a \Delta t$$
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$$v \int^{v(t)}_{v(0)} = v(t) - v(0) = a \times \int^t_0 = a \times (t - 0)$$
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$$\Rightarrow v(t) - v(0) = a \times t \Rightarrow v(t) = v(0) + a \times t$$
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$$v_x = \frac{\Delta x}{\Delta t}$$
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$$x(t) = x(0) + v(0) \times t + \frac{1}{2}at^2$$
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Zeitfreie:
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$$x(t)-x(0) = \frac{v(t)^2 - v(0)^2}{2a}$$
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(Script: Spezialfall $x = \frac{v^2}{2a}$, $x(0) = v(0) = 0$)
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