The speed of a regional airliner during its take off run is a=A-Bv^2. Where v is its speed and A and B are positive constants.
1. Starting from rest, how long does it take the airliner to reach its take off speed vr?
2. Find the speed v(t) during the take off as a function of time.
3. Find the distance st that the airliner requires to take off.
I think I understand the kinematics theory in this question I just really struggled with the integration. Any help would be amazing.
Since a(t) = dv / dt, we have a differential equation dv / dt = A - Bv^2. It can be solved using separation of variables. This gives v(t) and answers 2. Answering 1 involves finding the inverse of v(t). Answering 3 requires finding where t is the answer to question 1.