Question

1. how far in meters must a runway be in order for a plane to accelerate from rest to a velocity of 75 m/s if the plane can accelerate at 1.5 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. Here, $v_{0} = 0$ m/s (starts from rest), $v = 75$ m/s, and $a=1.5$ m/s².

Step2: Rearrange the equation for $x$

Since $v_{0} = 0$, the equation simplifies to $v^{2}=2ax$. Rearranging for $x$, we get $x=\frac{v^{2}}{2a}$.

Step3: Substitute the values

Substitute $v = 75$ m/s and $a = 1.5$ m/s² into the formula: $x=\frac{75^{2}}{2\times1.5}$.
First, calculate $75^{2}=5625$. Then, $2\times1.5 = 3$. So, $x=\frac{5625}{3}=1875$ m.

Answer:

1875 m