Questions: A plane takes off with a 35.1 m/s velocity after it advanced 1233.6 m of the road, if the plane was totally still at the beginning. Calculate the acceleration of the plane.

A plane takes off with a 35.1 m/s velocity after it advanced 1233.6 m of the road, if the plane was totally still at the beginning. Calculate the acceleration of the plane.

Transcript text: A plane takes off with a $35.1 \mathrm{~m} / \mathrm{s}$ velocity after it advanced 1233.6 m of the road, if the plane was totally still at the beginning. Calculate the acceleration of the plane. Answer: $\square$

Solution

Solution Steps

Step 1: Identificar la fórmula adecuada

Para calcular la aceleración del avión, podemos usar la fórmula de la cinemática que relaciona la velocidad final ($v_f$), la velocidad inicial ($v_i$), la aceleración ($a$) y la distancia recorrida ($d$):

\[ v_f^2 = v_i^2 + 2ad \]

Step 2: Sustituir los valores conocidos

Sabemos que:

La velocidad inicial ($v_i$) es $0 \, \mathrm{m/s}$ (el avión estaba totalmente quieto).
La velocidad final ($v_f$) es $35.1 \, \mathrm{m/s}$.
La distancia ($d$) es $1233.6 \, \mathrm{m}$.

Sustituimos estos valores en la fórmula:

\[ (35.1 \, \mathrm{m/s})^2 = (0 \, \mathrm{m/s})^2 + 2a(1233.6 \, \mathrm{m}) \]

Step 3: Resolver para la aceleración

Primero, calculamos $ (35.1 \, \mathrm{m/s})^2 $:

\[ 35.1^2 = 1232.01 \, \mathrm{m^2/s^2} \]

Luego, sustituimos y resolvemos para $a$:

\[ 1232.01 = 2a \cdot 1233.6 \]

\[ a = \frac{1232.01}{2 \cdot 1233.6} \]

\[ a = \frac{1232.01}{2467.2} \]

\[ a \approx 0.4993 \, \mathrm{m/s^2} \]