A small turbo-prop commuter airplane, starting from rest on a Gander airport runway, accelerates for 19.5 s before taking off. Its speed at takeoff is 53.6 m/s (120 mi/hr). Calculate the acceleration of the plane, in g's, assuming it remains constant. (i.e., divide the acceleration in m/s2 by 9.81 m/s2).
To solve this problem, we can use the kinematic equation that relates acceleration, initial velocity, final velocity, and time:
v = u + at
Where:
v = final velocity (53.6 m/s)
u = initial velocity (0 m/s, as the plane starts from rest)
a = acceleration
t = time (19.5 s)
Rearranging the equation, we get:
a = (v - u) / t
Substituting the given values:
a = (53.6 m/s - 0 m/s) / 19.5 s
a = 2.75 m/s²
Now, to calculate the acceleration in g's, we need to divide this value by the acceleration due to gravity (9.81 m/s²):
Acceleration in g's = a / g
Acceleration in g's = 2.75 m/s² / 9.81 m/s²
Calculating this, we find:
Acceleration in g's ≈ 0.28 g's
Therefore, the acceleration of the plane, assuming it remains constant, is approximately 0.28 g's.