How Do You Calculate the Motion and Velocity of a Falling Object with Drag?

[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.

 

[berkeman]

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.

The accelerating force and the drag force are in opposite directions, so they should have opposite signs.

 

[gneill]

If you can write an expression for the total acceleration, you'll be away to the races.

 

[ashishsinghal]

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

drag is opposite to velocity. velocity is in direction of g. Right. hence you cannot write m(dv/dt)=-mg-mkv. also dv/dt is +ve, this means
m(dv/dt)= mg - mkv