# Rate of change of distance from origin?

1. Aug 17, 2008

### avr10

1. The problem statement, all variables and given/known data

A particle moves along the parabola $$y = 4x^{2}$$ such that it's x coordinate increases at a steady rate of 5 units/minute.
How fast is the particle's distance from the origin changing when it is at the point (1,4)?

2. Relevant equations

3. The attempt at a solution

I honestly have no idea how to start this problem. A couple of ideas that pop up in my head are to take the derivatives $$\frac {dx}{dt}$$ and $$\frac {dy}{dt}$$ and use them to take the derivative of the distance formula from the origin, but there is no t...

I have no idea. Someone help get me started?

2. Aug 17, 2008

### dynamicsolo

Go with that thought. You have two pieces of information:
the distance of a point (x,y) from the origin is given by $$s^2 = x^2 + y^2$$ and the position of a point (x,y) on the parabola is (x, x^2).

You will be interested in ds/dt. Differentiate the distance equation implicitly with respect to t after making the appropriate substitutions.

If you haven't had implicit differentiation yet, no matter. Make the appropriate substitutions into the distance equation and you will have the distance as a function of x only, which you can then solve for s and differentiate with respect to t.

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