Is there any gravity? Is the rocket working against gravity? If so, are you assuming that the gravitational force is constant, or does the inverse square thing?
In this problem I have a rocket that is accelerated from rest by thrust that varies with time according to: F=1000t, if 0<t<2.
I need to find velocity equation for the rocket if mass remains constant and the drag force is equal to ten times its velocity. Mass of the rocket is 1600 lb.
What I did so far:
m(dv/dt)=F-kv
After trying to separate variables I end up with:
dv + (kv/m)dt = (1000t/m)dt
As you can see I am not able to separate variables, and it does not look like diff. equation of the first order.
Can you help me?
Thank you.
m(dv/dt)=F-kv
dv/dt+(k/m)v=F/m (This fits into standard form of diff. equation of first order, where P=k/m, and Q=F/m)
∫Pdt=(k/m)t
e^∫Pdt=e^(k/m)t
ve^(k/m)t = ∫(F/m) e^(k/m)t dt
After integrating right side, solving for v, and substituting in given values I get:
v=100t+Ce^-t/160
Does this make sense?
Thank you.
Plug your solution back into the DE and see if it satisfies it. This is a standard step to perform when solving any DE. It's usually quite straight-forward to do (differentiation is generally easier than integration), and it prevents mistakes. So, what do you get?