# Calculating Rate of Change of Distance to Origin

• Weave
In summary, the conversation is about finding the rate of change of the distance from a moving particle to the origin, given its position on a curve and its rate of change in the x-coordinate. The solution involves finding a formula for distance, plugging in known values, and differentiating to find the desired rate of change.

## Homework Statement

A particle is moving along the curve $$y= 3 \sqrt(4 x + 4)$$. As the particle passes through the point (3, 12), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

## Homework Equations

1.$$y= 3* \sqrt(4 x + 4)$$

## The Attempt at a Solution

Not too sure how to start.

Begin with a formula for the distance(D) from (x,y) to the origin. Then you can plug in what you know about y. Finally differentiate (implicitly) the formula with respect to time. You should get an equation involving dD/dt, x, and dx/dt. You know x, and dx/dt. Find dD/dt.

What formula for distance are you talking about?

Weave said:
What formula for distance are you talking about?

No wonder you are having a problem! When dealing with "distance to the origin", you really need to know that the distance from a point (x,y) to the origin, (0,0), is $\sqrt{x^2+ y^2}$!

## What is rate of change of distance to origin?

Rate of change of distance to origin refers to the speed at which an object is moving away from or towards the origin point. It is a measure of the change in distance over a specific period of time.

## How is rate of change of distance to origin calculated?

To calculate the rate of change of distance to origin, you need to determine the change in distance and time. Then, divide the change in distance by the change in time. This will give you the average rate of change over the given time interval.

## What is the unit of measurement for rate of change of distance to origin?

The unit of measurement for rate of change of distance to origin is distance per unit time, such as meters per second or kilometers per hour.

## Why is rate of change of distance to origin important in science?

Rate of change of distance to origin is important in science because it helps us understand the motion of objects and how they change over time. It is a fundamental concept in physics and is used to study the movement of objects, such as in kinematics and dynamics.

## Can rate of change of distance to origin be negative?

Yes, rate of change of distance to origin can be negative. This indicates that the object is moving towards the origin or decreasing in distance from the origin over time. A positive rate of change indicates that the object is moving away from the origin or increasing in distance from the origin over time.