A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.



Answer to a math question A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.

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Para calcular la aceleración, utilizamos la fórmula de aceleración:

a = \frac{v_f - v_i}{t}

a = aceleración
v_f = velocidad final
v_i = velocidad inicial
t = tiempo

En este caso, la velocidad inicial (v_i) es igual a 30 km/h, la velocidad final (v_f) es igual a 0 km/h (ya que el autobús se detiene por completo) y el tiempo (t) es igual a 15 segundos.

Convertimos la velocidad de km/h a m/s:
v_i = 30 \times \frac{1000}{3600} = 8.33 \, \text{m/s}

Sustituimos los valores en la fórmula de aceleración:
a = \frac{0 - 8.33}{15} = -0.55 \, \text{m/s}^2

Por lo tanto, la aceleración del autobús es de -0.55 \, \text{m/s}^2.

Para calcular la fuerza que actúa sobre el cuerpo, utilizamos la segunda ley de Newton:

F = m \cdot a

F = fuerza
m = masa
a = aceleración

En este caso, la masa (m) del autobús es de 20,000 kg y la aceleración (a) es de -0.55 m/s^2.

Sustituimos los valores en la fórmula de la fuerza:
F = 20,000 \cdot (-0.55) = -11,000 \, \text{N}

Por lo tanto, la fuerza que actúa sobre el cuerpo del autobús es de -11,000 \, \text{N}.

La aceleración del autobús es de -0.55 \, \text{m/s}^2 y la fuerza que actúa sobre el cuerpo es de -11,000 \, \text{N}.

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