# Position vector R of a particle moving x-y plane

• chris61986
In summary, the conversation is about a person asking for help with their UPI homework. They are trying to calculate the position, velocity, and acceleration of a particle in the x-y plane using the given equation. They want to confirm if their method is correct. The expert confirms that their approach is correct and reminds them that r is a vector.
chris61986
Hello, new to these forums! I'm working on my UPI homework, and I just want to verify if I'm doing something correctly. The problem:

The position vector r of a particle moving in the x - y plane given by r = (2t^3)i + (6-7t^4)j, where r is in meters and t is in seconds.
Calculate
r
v
a
when t = 2s

Now, I'm pretty sure I know how to do it, but I don't get a second chance once I turn the homework in! :)

So in the original equation, r is meters. So I'm thinking this is the displacement.
If this is the displacement, I just plug in 2 for t and solve.
Because that's the displacement, I can find a and v from the derivatives of the original function.

Is this correct?

Sounds good. Just remember that $\vec r$ is a vector.

## 1. What is a position vector?

A position vector is a mathematical representation of the location of a particle or object in space. It is typically denoted by the symbol R and contains both magnitude and direction information.

## 2. How is a position vector different from a displacement vector?

A position vector represents the current location of an object in space, while a displacement vector represents the change in position from one location to another. In other words, a displacement vector is the difference between two position vectors.

## 3. How is a position vector used in the x-y plane?

In the x-y plane, a position vector is commonly used to represent the location of an object with respect to a fixed origin point. The x and y components of the position vector indicate the horizontal and vertical distance from the origin, respectively.

## 4. How do you calculate the magnitude of a position vector?

The magnitude of a position vector is calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the x and y components. In equation form, this can be written as |R| = √(x2 + y2).

## 5. Can a position vector have a negative magnitude?

No, a position vector cannot have a negative magnitude. The magnitude of a position vector is always a positive value, as it represents the distance from the origin to the object's location in space. However, the x and y components of a position vector can be negative if the object is located in the negative x or y direction from the origin.

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