# Find Speed of Particle: Position Function r(t)= et(cos(t)i+sin(t)j+7tk)

• julz3216
In summary, the conversation discusses finding the speed of a particle with a given position function, using the derivative of the function. The individual is having trouble finding the correct solution and is seeking guidance.
julz3216

## Homework Statement

Consider the following position function.
r(t)= et(cos(t)i+sin(t)j+7tk)

Find the speed of a particle with the given position function.

## Homework Equations

I know I take the derivative of the function but I can't seem to get speed.
I got v=e^t(cos(t)i+sin(t)j+7(t)k)+ e^t(-sin(t)i+cos(t)j+7k)

## The Attempt at a Solution

I just can't find the speed, i think i may be just slightly off. I currently have speed is 7e^t(t+1) which is wrong.

Edit:

You are simply using "k" part, where is your i and j part. They don't cancel out.

Last edited:

## 1. How do I find the speed of a particle using the position function r(t)?

To find the speed of a particle using the position function r(t), you can use the formula speed = magnitude of velocity = ||v(t)|| = √(v(t) · v(t)).

## 2. What is the significance of the "t" in the position function r(t)?

The "t" in the position function r(t) represents time. It is a variable that allows us to track the position of the particle at different points in time.

## 3. Can the position function r(t) be used to find the speed of a particle at a specific time?

Yes, the position function r(t) can be used to find the speed of a particle at a specific time by plugging in the value of t into the formula for speed.

## 4. How does the position function r(t) differ from the velocity function v(t)?

The position function r(t) gives the position of the particle at a specific time, while the velocity function v(t) gives the instantaneous rate of change of position at a specific time.

## 5. Can the position function r(t) be used to determine the acceleration of a particle?

No, the position function r(t) alone cannot be used to determine the acceleration of a particle. To find acceleration, you would need the velocity function v(t) and take the derivative of it with respect to time.

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