Question

An airplane accelerates down a runway at 4 m/s² for 28.7 seconds until it finally lifts off the ground. Assuming the plane started at rest, what was the displacement of the plane before takeoff?

a) 7 m
b) 1647 m
c) 122 m
d) 3295 m

Answer 1

The displacement of the airplane before takeoff is 1647 m (Option b), calculated using the kinematic equation for displacement with the given acceleration and time.

Step-by-step explanation:

The student is asking about the displacement of an airplane which accelerates uniformly down a runway. Given that the plane starts from rest and accelerates at 4 m/s² for 28.7 seconds before takeoff, we can use the kinematic equation for displacement (s = ut + (1/2)at²) where u is the initial velocity, a is the acceleration, and t is the time. The plane starts at rest, so u = 0, and with t = 28.7 s and a = 4 m/s², the displacement s is computed as:

s = 0 + (1/2)(4 m/s²)(28.7 s)²

s = 2 m/s² × 822.49 s²

s = 1644.98 m, which can be rounded to 1647 m (Option b).