# Motion in the Presence of Velocity-Dependent Resistive Forces

1. Oct 5, 2007

### twotaileddemon

1. The problem statement, all variables and given/known data

A small piece of Styrofoam packing material is dropped from a height of 2.10 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g - bv. After falling 0.400 m, the styrofoam effectively reaches terminal speed, and then takes 4.90 s more to reach the ground.

(a) What is the value of the constant b?
(b) What is the acceleration at t = 0?
(c) What is the acceleration when the speed is 0.150 m/s?

2. Relevant equations

a = g - bv
R = -bv
Terminal speed = g/b

3. The attempt at a solution
I'm, ah.. very stuck on this.
I know for sure (b) is 9.8 m/s (down) because when t = 0 v = 0, and thus the acceleration is just the gravity constant
I thought I could using vf^2 = vi^2 + 2a(yf-yi) or y_f = y_o + at to find the acceleration... but those equations don't seem to fit that well.
If have a feeling if I knew (a) I could find (c) but I'm just lost.. especially without a mass or terminal velocity.

I appreciate any help~

2. Oct 6, 2007

### hotvette

Since you know the terminal speed, the following will allow you to calculate b:

After falling 0.400 m, the styrofoam effectively reaches terminal speed, and then takes 4.90 s more to reach the ground.

By the way, how did you determine the terminal speed in relevant equations?

Last edited: Oct 6, 2007
3. Oct 6, 2007

### twotaileddemon

Ah.. um, thanks for your help~ but I found the answer a while ago and forgot I posted this
^_^