Question : related rates particle moving along a curve?
A particle is moving along the curve y = 4(4x+4)^(1/2) . As the particle passes through the point (3,16) its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
moving rates

Best answer:

Answer by brucerl@pacbell.net
1. Use the distance formula s = √( x^2 + y^2 )

2. Use the equation which you provided to substitute for y

3. Differentiate s with respect to time ( find ds/dt)
When you differentiate, think of x as being a function of time that you need to use the chain rule on. Since you don’t know what this function is you write dx/dt wherever you want to take the derivative of x with respect to t.

4. You are told that the x-coordinate increases at a rate of 5 units per second. This means that dx/dt = 5 unit per second. Substitute this in what you have from step 3.

5. They want ds/dt at the point (3,16) so substitute x = 3