Solving ODEs for Velocity & Limiting Velocity

[keelejody]

i have a question but no mark scheme so i can't see where I am going wrong. a mass, m, is dropped with speed zero from point O at time t=0 after time t it has traveled x. the body is subject to acceleration due to gravity and drag -mkv.

(A) write the equation of motion:

ok so i know v=dx/dt

and I've said f=m(dv/dt)

so f=m(dv/dt)=-mg-mkv? because theyre opposite

I can't think what else to write, since this is 5 marks... unless i need sort this in terms of ODE's where g and k are constants?

(B) calculate velocity as a function of time, and the limiting velocity at very large time.

so i need v(t)? from v=dx/dt and this is where i use ODE's and work out V.

again i can't see where the marks come from this is worth 8.

 

[hologramANDY]

I think you are missing half of your equation here

"f=m(dv/dt)=-mg-mkv"

"-mg-mkv" is the f side of the equation, because those are the forces acting on it. You are missing the values for the m(dv/dt) side.

F = m(dv/dt)
-mg-mkv = ?

Also, you aren't supposed to post homework here, there is a special thread for that.

 

[keelejody]

thanks I am still new to stuff and thanks