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I am having a difficult time getting far into solving this problem:

"A small piece of Styrofoam packing material is dropped from a height of 2.00 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g - bv. After falling 0.500 m, the Styrofoam effectively reaches terminal speed, and then takes 5.00 s more to reach the ground. (a) What is the value of the constantb? (b) What is the acceleration at t = 0? (c) What is the accleration when the speed is 0.150 m/s?"

The first thing I did is to draw a free-body diagram of the Styrofoam falling, with the resisitive forces pointing upward, and the weight pointing downward. Making downward being positive, the resistive forces are negative (hence the given accleration being a = g - bv).

To find b, I first need to find velocity and I don't see how I could find that. I tried setting mg - bv = m(g -bv) = m(v^2/r). This seems kind of messy, but if it's necessary, I would think velocity and mass would eventually cancel out. Is this the right way of solving this problem?

I also thought about using a free-fall kinematic equation and simply solving for velocity, but I think those are appropriate for problems that neglect air resistance. Am I correct?

Thank you.

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# Homework Help: Motion In the Presence of Resistive Forces

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