Instantaneous Acceleration in 2D Video Lessons

Concept

# Problem: Using a reference frame with the origin at the take-off airport, the positive x-axis due East, and the positive y-axis due North, the acceleration a of an airplane as a function of time can be described as: a = (αt)î + (βt 4 − γt)ĵ, with α, β, and γ positive and constant. Assuming that the airplane takes off from the airport at time t = 0 with zero initial velocity: a) What are the units of α, β, and γ? b) Find the time(s) when the airplane position is directly NE of the airport. c) Find the trajectory of the plane, y(x). Write your results in terms of α, β, and γ. Remember to check the dimensions/units for each answer.

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###### Problem Details

Using a reference frame with the origin at the take-off airport, the positive x-axis due East, and the positive y-axis due North, the acceleration a of an airplane as a function of time can be described as:

a = (αt)î + (βt 4 − γt)ĵ,

with α, β, and γ positive and constant.

Assuming that the airplane takes off from the airport at time t = 0 with zero initial velocity:

a) What are the units of α, β, and γ?

b) Find the time(s) when the airplane position is directly NE of the airport.

c) Find the trajectory of the plane, y(x).

Write your results in terms of α, β, and γ. Remember to check the dimensions/units for each answer.