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question 13 of 26
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the minimum takeoff speed for a certain airplane is 75 m/s. what minimum acceleration is required if the plane must leave a runway of length 1050 m? assume the plane starts from rest at one end of the runway.
2.7 m/s²
4.5 m/s²
6.0 m/s²
1.5 m/s²
3.0 m/s²

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v^{2}=v_{0}^{2}+2ax$, where $v$ is the final velocity, $v_{0}$ is the initial velocity, $a$ is the acceleration, and $x$ is the displacement.

Step2: Substitute the given values

Given $v = 75\ m/s$, $v_{0}=0\ m/s$ (starts from rest), and $x = 1050\ m$. Substituting into the equation $v^{2}=v_{0}^{2}+2ax$, we get $(75)^{2}=0^{2}+2a\times1050$.

Step3: Solve for acceleration $a$

First, expand the equation: $5625 = 2100a$. Then, solve for $a$: $a=\frac{5625}{2100}\approx2.7\ m/s^{2}$.

Answer:

$2.7\ m/s^{2}$