
#1
Oct2107, 02:18 PM

P: 18

1. The problem statement, all variables and given/known data
Let c be a path in R^3 with zero acceleration. Prove that c is a straight line or a point. 2. Relevant equations F(c(t)) = ma(t) a(t) = c''(t) 3. The attempt at a solution so i know that since the acceleration is zero, the velocity must be constant, and when you integrate a constant, you get a straight line...but how to I prove mathematically that the velocity is constant, because you can't integrate 0dt, as far as I know? 



#2
Oct2107, 02:20 PM

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PF Gold
P: 12,016

The indefinite integral, i.e, the antiderivative of 0 is, indeed, a constant; that is we have:
[tex]\int{0}dx=C[/tex] 



#3
Oct2107, 02:30 PM

P: 18

oh ok, so if I integrate that again I get that c(t) = Ct + D, which fits the general equation for a line
but then, does that also prove that c(t) could just be a single point? 



#4
Oct2107, 02:47 PM

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PF Gold
P: 12,016

Zero Acceleration
Indeed, since big C could be..0!




#5
Oct2107, 03:00 PM

P: 18

oh. duh!
gratzie 



#6
Oct2107, 05:27 PM

Math
Emeritus
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Thanks
PF Gold
P: 38,882




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