Finding Rectangular Coordinates

In summary, the problem involves a particle's position, velocity, and acceleration given by a vector ~r = (5t^3, 3t − 6t^4)m as a function of time in seconds. The rectangular coordinates at t = 2.5 s can be found by substituting t = 2.5 into the vector components. The relationship between distance, velocity, and acceleration functions is that velocity is the derivative of distance and acceleration is the derivative of velocity. The expressions for velocity and acceleration in Cartesian coordinates can be derived from the distance function.
  • #1
Jordash
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Homework Statement



A particle moves with position as a function of time in seconds given by the vector ~r = (5t^3, 3t − 6t^4)m.

What are the rectangular coordinates of the particle’s position at t = 2.5 s?
What are the rectangular coordinates of the particle’s velocity at t = 2.5 s?
What are the rectangular coordinates of the particle’s acceleration at t = 2.5 s?

Homework Equations





The Attempt at a Solution



I'm a little bit lost? I know that the Vector Components is rx=(5t^3) and ry=6t^4 is that right, so I know I plug in numbers to find the vectors but I don't know which ones?
 
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  • #2
What's the relationship between distance, velocity and acceleration functions?
 
  • #3
I'm not sure what that means but it says something like this:

Derive expressions for the velocity and the acceleration of the particle as function of time in
Cartesian coordinates.
 
  • #4
Yes I am asking if you have a function that tells you distance, how do you get velocity function?, how do you get acceleration function?
 

1. What are rectangular coordinates?

Rectangular coordinates, also known as Cartesian coordinates, are a system of representing a point or location in a plane by using two numbers, typically x and y, to specify its position.

2. How do you find rectangular coordinates?

To find rectangular coordinates, you need to determine the x-coordinate and y-coordinate of the point or location. This can be done by drawing a vertical line from the point to the x-axis and a horizontal line from the point to the y-axis. The coordinates of the point are where these lines intersect the x-axis and y-axis, respectively.

3. What is the difference between polar coordinates and rectangular coordinates?

Polar coordinates use a distance from the origin and an angle from a reference direction to represent a point, while rectangular coordinates use two perpendicular axes and two numbers to represent a point. Polar coordinates are often used in situations where direction and distance are more important than horizontal and vertical position, while rectangular coordinates are used for more precise positioning.

4. Can rectangular coordinates be negative?

Yes, rectangular coordinates can be negative. The x-coordinate represents horizontal position and can be positive or negative depending on whether it is to the right or left of the y-axis. The y-coordinate represents vertical position and can also be positive or negative depending on whether it is above or below the x-axis.

5. How are rectangular coordinates used in real life?

Rectangular coordinates are used in many real-life applications, such as navigation and mapping, computer graphics, and engineering. They can also be used to represent physical quantities, such as position, velocity, and acceleration, in mathematical equations and models.

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