Word problem Derivative of Distance formula Super hard. Please help.

In summary, the problem involves finding the derivative of the distance formula, given a point P moving along the curve y=√x and increasing at a rate of 40 units/s when x=3. The task is to determine the speed at which the distance between P and the point (2,0) is changing at that instant. The solution involves using the distance formula and finding the distance between P and (2,0).
  • #1
algar32
89
1
Word problem Derivative of Distance formula... Super hard. Please help.

Homework Statement



A point P is moving along the cruve whose equation is y=√x. Suppose that x is increasing
at the rate of 40 units/s when x=3. How fast is the distance between p and the point (2,0) changing\
at that instant?


Homework Equations


Distance forumula


The Attempt at a Solution


Not even posting it... Its completely wrong


Can you please show me how to do this? Show your work please.

Thanks you.
 
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  • #2


Sorry I meant to say curve... not cruve.
 
  • #3


Let's call the distance between P and (2,0) as s and P has the coordinates (x,y).

What is the distance between P and (2,0) ? (Use your distance formula here)
 
  • #4


i got it
 

1. What is the distance formula and how is it used?

The distance formula is a mathematical equation used to determine the distance between two points in a coordinate plane. It is often used in geometry and physics to calculate the distance traveled by an object or the distance between two objects.

2. What is a derivative and how does it relate to the distance formula?

A derivative is a mathematical concept that measures the rate of change of a function. In the context of the distance formula, the derivative can be used to calculate the instantaneous rate of change of the distance between two points at any given point in time.

3. How do you take the derivative of the distance formula?

The distance formula can be expressed as a function of time, with the distance between two points being a function of time. To take the derivative of this function, you would use the power rule, product rule, or chain rule, depending on how the formula is written.

4. Why is finding the derivative of the distance formula considered super hard?

Finding the derivative of the distance formula can be considered difficult because it requires a strong understanding of calculus and the various rules and techniques used in taking derivatives. It also involves manipulating complex equations and understanding how they relate to real-world scenarios.

5. What are some real-world applications of using the derivative of the distance formula?

The derivative of the distance formula has many real-world applications, including determining the velocity and acceleration of moving objects, calculating the slope of a curve, and finding the rate of change in various physical systems. It is also used in fields such as engineering, physics, and economics.

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