Question

An airplane initially travels at 15 m/s when passing the ""acceleration line"". The airplane then accelerates at 8.00 m/s2 until reaching its take off velocity of 50.0 m/s. What is the displacement of the plane during the acceleration?"

Answer 1

To calculate the displacement during the acceleration, we use the kinematic equation v_f^2 = v_i^2 + 2ad, where the initial and final velocities are 15 m/s and 50 m/s, respectively, with an acceleration of 8.00 m/s^2. The displacement is found to be approximately 142.2 meters.

Step-by-step explanation:

The displacement of the plane during the acceleration can be found using the kinematic equation which relates initial velocity, final velocity, acceleration, and displacement. We have the initial velocity (vi) of the plane as 15 m/s, the final velocity (vf) as 50 m/s, and the acceleration (a) as 8.00 m/s2. Using the equation vf2 = vi2 + 2ad where d is displacement, we can solve for d:

• (50 m/s)2 = (15 m/s)2 + 2(8.00 m/s2)d
• 2500 m2/s2 = 225 m2/s2 + 16 m/s2d
• 2500 m2/s2 - 225 m2/s2 = 16 m/s2d
• d = (2500 m2/s2 - 225 m2/s2)/16 m/s2
• d = 2275 m2/s2 / 16 m/s2
• d = 142.1875 m

The displacement of the airplane during its acceleration is therefore approximately 142.2 meters.