2.7 There are certain simple one-dimensional problems where the equation of motion (Newton'ssecond law) can always be solved, or at least reduced to the problem of doing an integral. One of these(which we have met a couple of times in this chapter) is the motion of a one-dimensional particle subjectto a force that depends only on the velocity v, that is, F = F(v). Write down Newton's second law andseparate the variables by rewriting it as m dv/F(v) = dt. Now integrate both sides of this equation andshow thatt = mv dv'F(v¹)VoProvided you can do the integral, this gives t as a function of v. You can then solve to give v as afunction of t. Use this method to solve the special case that F(v) = Fo, a constant, and comment onyour result. This method of separation of variables is used again in Problems 2.8 and 2.9.

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