Particle Dynamics and Time Problem

[s4orce]

When a particle fall through the air, its initial acceleration a=g diminishes until it is zero, and thereafter it falls at a constant or terminal velocity vf. If this variation of the acceleration can be expressed as a=(g/v^2f)(v^2f-v^2), determine the time needed for the velocity v<vf. Initially the particle falls from rest.

 

[Pyrrhus]

did you mean find the time when v=vf or terminal velocity?

 

[s4orce]

find the time for the velocity to become v<vf. (V less than Vf)

 

[Pyrrhus]

So, how are you going to start the problem?

 

[s4orce]

make the forces and gravitation = to each other? can you help me please?

 

[Pyrrhus]

make the forces and gravitation = to each other? can you help me please?

Start up by setting the ordinary differential equation, dv/dt.

 

[s4orce]

dv/dt = (g/v^2f)(v^2f-v^2)? like that? how? can you please show me

 

[Pyrrhus]

Ok now, when will v be less than the terminal velocity?