# Particle Dynamics and Time Problem

## Main Question or Discussion Point

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.

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

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

Pyrrhus
Homework Helper
So, how are you going to start the problem?

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

Pyrrhus
Homework Helper
make the forces and gravitation = to eachother? can you help me please?
Start up by setting the ordinary differential equation, dv/dt.

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

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