A small body of mass m located near the Earth’s surface falls from rest in the Earth's gravitational field. Acting on the body is a resistive force of magnitude kmv, where k is a constant and v is the speed of the body.(adsbygoogle = window.adsbygoogle || []).push({});

a) Write the differential equation that represents Newton's second law for this situation.

my answer: F = ma

a = dv/dt

F = mg - kmv

ma = mg - kmv

a = g - kv

dv/dt = g - kv

I'm pretty sure I got this one right.

b) Determine the terminal speed v_{T}of the body.

F = 0

g - kv = 0

g = kv

v_{T}= g / k

I think I got this one right too.

c) Integrate the differential equation once to obtain an expression for the speed v as a function of time t. Use the condition that v = 0 when t= 0.

What I did so far:

dv/dt = g - kv

dt = dv / (g - kv)

So I would integrate dt = dv / (g - kv). The problem is I don't know how. Can someone please explain how to do this kind of integration, why I would do it that way?

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# Homework Help: Terminal velocity of a body of mass

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