# Particle Dynamics Problem

1. Jan 30, 2007

### 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.

2. Jan 30, 2007

### Pyrrhus

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

3. Jan 30, 2007

### s4orce

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

4. Jan 30, 2007

### Pyrrhus

So, how are you going to start the problem?

5. Jan 30, 2007

### s4orce

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

6. Jan 30, 2007

### Pyrrhus

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

7. Jan 30, 2007

### s4orce

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

8. Jan 30, 2007

### Pyrrhus

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