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Dx/dt = 3 m/s solve for x(t)

  1. Feb 17, 2010 #1
    Hello out there,and pardon my dementia but:

    I am a middle aged guy, bordering well on old now, who graduated from professional school in 1986 and I was already an older than most student at that time. I had one semester of calculus in 1973 and slipped through with a C major.
    My calculus is limited to very basic diff and integ and a young upstart resident handed me this today:

    dx/dt = 3 m/s solve for x(t)

    I am lost. The answer is not zero or some constant I am sure. The two variable business changes everything, right?

    If this is a differential equation, nothing in my old notes is helping to enlighten me. Any help would be appreciated.
    If this upstart resident has made a fool of me and the problem is bogus, he will regret it. He says he could not answer it so I don't know what is up his sleeve. I'm thinking that the problem may be just a lot of bull.Thank you. CTF
  2. jcsd
  3. Feb 17, 2010 #2
    I will bite.

    Integrate both sides to obtain:

    [tex]\int_{x'=0}^{x} dx' = \int_{t'=0}^{t} 3 dt'[/tex]

    That is, [tex] x' |_{0}^{x} = 3 t' |_{0}^{t} \implies x(t) = 3t[/tex].

    Edit: I post this full solution because I believe the question is simple enough that there's no point beating around the bush.
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