An airplane accelerates down a runway at 3.33 m/s2 for 35.3 s until is finally lifts off the ground. Determine the distance traveled before takeoff.
d=1/2 a t^2
To determine the distance traveled before takeoff, you can use the kinematic equation:
d = v0t + (1/2)at^2
Where:
d = distance traveled
v0 = initial velocity (in this case, 0 m/s since the airplane starts from rest)
t = time
a = acceleration
Given:
v0 = 0 m/s
a = 3.33 m/s²
t = 35.3 s
Substituting the values into the equation, we get:
d = (0)(35.3) + (1/2)(3.33)(35.3^2)
Simplifying the equation:
d = 0 + (1/2)(3.33)(35.3^2)
Calculating the equation:
d = (1/2)(3.33)(1248.09)
d = 2074.1357 m
Therefore, the distance traveled before takeoff is approximately 2074.1357 meters.