Question

choose the equation that helps solve the following problem most easily... hark is employed as an engineer and is designing the runway for an airport. of the planes that will use the airport, the lowest acceleration rate will likely be 3 m/s2. the takeoff speed for this plane will be 65 m/s. assuming this minimum acceleration, what is the minimum allowed length for the runway? (hint: v0 = vf)
d = v0t + \frac{1}{2}at^{2} (hint: v0 = vf)
vf^{2}=v0^{2}+2ad (hint: v0 = vf)
d = \frac{v0 + vf}{2}\cdot t (hint: v0 = vf)
vf = v0 + at (hint: v0 = vf)

Explanation:

Step1: Identify given values

Initial velocity $v_0 = 0$ (assuming starts from rest), final velocity $v_f=65$ m/s, acceleration $a = 3$ m/s², and we need to find the distance $d$.

Step2: Analyze the equations

The equation $v_f^2=v_0^2 + 2ad$ is suitable as it relates final - velocity, initial - velocity, acceleration and distance without involving time $t$. Substituting $v_0 = 0$ into $v_f^2=v_0^2 + 2ad$, we get $v_f^2=2ad$, and we can solve for $d$.

Answer:

The equation $v_f^2=v_0^2 + 2ad$ helps solve the problem most easily.