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After starting, a subway should reach a speed of 50 km/h over a distance of 100 m. 1) what specific acceleration is necessary

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Answer to a math question After starting, a subway should reach a speed of 50 km/h over a distance of 100 m. 1) what specific acceleration is necessary

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Corbin
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Um die spezifische Beschleunigung zu berechnen, die eine U-Bahn benötigt, um auf einer Strecke von 100 m eine Geschwindigkeit von 50 km/h zu erreichen, können wir die kinematische Gleichung verwenden: v^2 = u^2 + 2as Wo: - \( v \) ist die Endgeschwindigkeit (50 km/h), - \( u \) ist die Anfangsgeschwindigkeit (0 km/h, vorausgesetzt, die U-Bahn startet aus dem Ruhezustand), - \( a \) ist die Beschleunigung, - \( s \) ist die Distanz, über die die Beschleunigung auftritt (100 m). Zuerst müssen wir die Endgeschwindigkeit in Meter pro Sekunde (m/s) umrechnen: 50 \text{ km/h} = \frac{50 \times 1000}{3600} \text{ m/s} = 13,89 \text{ m/s} Jetzt können wir die Werte in die Gleichung einsetzen und nach \( a \) auflösen: (13,89 \text{ m/s})^2 = (0 \text{ m/s})^2 + 2 \times a \times 100 \text{ m} 193,21 \text{ m}^2/\text{s}^2 = 200a \text{ m} a = \frac{193,21}{200} \text{ m/s}^2 a = 0,966 \text{ m/s}^2 Die spezifische Beschleunigung, die die U-Bahn benötigt, um über eine Distanz von 100 m eine Geschwindigkeit von 50 km/h zu erreichen, beträgt also ungefähr \( 0,966 \text{ m/s}^2 \).

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