(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose the acceleration of a particle is a function of x, where a_{x}(x) = (2.0 s_{-2})x.

(a) If the velocity is zero when x = 1.0 m, what is the speed when x = 2.7 m?

(b) How long does it take the particle to travel from x = 1.0 m to x = 2.7 m?

2. Relevant equations

a = integral v dt = integral (integral (x)) dt

3. The attempt at a solution

This CAN be solved as a differential equation, but we haven't done those in my Calc course yet, so I have no idea how to solve it that way.

On the other hand, I know the problem is that acceleration is a function of x, hence a(x), and that it needs to be a function of time in order to change it over to velocity and then displacement (if needed). So, I tried figuring that out and go to this point:

a = [tex]\frac{dv}{dt}[/tex] = ([tex]\frac{dv}{dx}[/tex] * [tex]\frac{dx}{dt}[/tex])

[tex]\int\frac{dv}{dx}[/tex] = [tex]\int2x[/tex][tex]\frac{dx}{dt}[/tex]

v = x^{2}+ c

Do I have this set up correctly? And, if so, wouldn't the integral (and thus the velocity function) end up being x^{2}+ some constant? And would that constant be related to part b, or inherited from the given info?

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# Homework Help: Changing the Variable of Integration

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