Finding velocity with constant, incre., decrea, varying acce

[Noah Drakes]

Homework Statement

Force of jet= A(r(t))4/3
A: constant determined by the fighter model in the class being considered and the drag force on the plane
r(t): the rate of fuel consumption as a function of time

Consider 3 possible situations for r(t):

1. when the rate is constant for the duration of the acceleration period
2. when the rate is steadily decreasing for the duration of the acceleration period
3. when the rate decreases at a decreasing rate as the plane accelerates

For each of these you should assume that the rate is initially 500 ffu (fighter fuel units)/min,
and for each it is reasonable to suppose an acceleration period of 10 minutes.

Determine-in terms of the characteristics of the fighter (m and A)- the maximum velocity obtained by the jet

Homework Equations

F=ma

The Attempt at a Solution

I set F=ma equal to Fjet = A(r(t)^4/3. So ma=A(r(t)^4/3 .

Now i solved for "a" to get an equation for acceleration: a=(A(r(t)^4/3)/(m)

Then i differentiated the equation to get velocity : A/m * 3/7 (r(t) ^ (7/3)

confused on how to approach the problem from here. I have a test on wednesday with a problem similar to this problem. It would be immensly helpful if someone solved the problem explaining each step and why.

I am new to this community by the way.

 

[Noah Drakes]

i also want to point out i copied the question from someone else's forum, but the work is mine.