Newtons laws: Seem's simple but not for me

[premsantosh]

Homework Statement

given initial coordinates, r(0), r'(0) and F(r,r',t)
find r(t)

Homework Equations

r''(t) = F(r(t), r'(t), t) / m

The Attempt at a Solution

have no idea where to start. some hint please, seem's pretty simple but not striking me.

 

[tiny-tim]

hi premsantosh!

what is F ?

 

[premsantosh]

Am sorry for not explaining the variables.
F = force
r is the position
r' is the velocity
r'' is the acceleration
t is the time
m is the mass

so essentially the first equation is: a = F/m

 

[tiny-tim]

yes i know, but what function is F ?

 

[premsantosh]

I am not sure what your question is but I am assuming you are referring to F(r,r',t)
If its that then I am sorry that's what I do not understand too :P
Since it says F is dependent on the position, velocity at the current time t, I think we can maybe use some kind of equations to solve??

 

[tiny-tim]

F could be any function of r r' and t …

you need to know what it is before you can solve it

where did you get this question from?

 

[willem2]

I am not sure what your question is but I am assuming you are referring to F(r,r',t)
If its that then I am sorry that's what I do not understand too :P
Since it says F is dependent on the position, velocity at the current time t, I think we can maybe use some kind of equations to solve??

There's no general solution for all F. There's lots of solutions for specific F. Most of them are when F is independent of t.

F = C. Solution r(t) = r(0) + r'(o)t + 1/2 (C/m) t^2
F = -kr(t). Solution r = A sin(B + Ct)

etc.