Position Vectors, Velocity Vectors, and Acceleration Vectors

In summary: For part (a) you are asked to determine the components of velocity and acceleration at time t=0. This is done by taking the derivatives of the given position equations. In part (b), you are asked to write expressions for the position vector, velocity vector, and acceleration vector at any time t>0. This is done by using the given equations and eliminating the variable t. Finally, in part (c), you are asked to describe the path of the object in an xy plot. This can be done by graphing the position equations and observing the shape of the curve.
  • #1
niyati
63
0
The coordinates of an object moving in the xy plane vary with time according to the equations x = -(5.00 m)sin(wt) and y = (4.00 m) - (5.00 m)cos(wt), where w is a constant and t is in seconds. (a) Determine the components of velocity and components of acceleration at t = 0. (b) Write expressions for the position vector, the velocity vector, and the acceleration vector at any time t > 0. (c) Describe the path of the object in an xy plot.

(a) When time is zero, the positions of x and y are 0 and 4, respectively. I am wondering how I can determine a velocity of a vertical line. I don't think it is zero, as that would be a horizontal line, and to have no slope would mean that there isn't a velocity. Where there is no velocity, there is no acceleration, so to find the components would be impossible.

(b) My problem here is that there are two different equations dealing with the components. It is not an independent variable as x and the dependent variable as y. However, if I squared both equations, added them, and then took the square root (like find the length of the hypotenuse), would that be an equation for the position? And since it says at any time greater than zero, am I to take the derivative of such equation to get the velocity, and again for the acceleration?

(c) I...really don't know what to do with this part, but I'm positive that this has something to do with part (b) (...duh), which, well, I'm not getting either.

I think I'm over-complicating things, especially in part (b), because nothing in this portion of my chapter (...the beginning) did anything this weird.

Help?
 
Physics news on Phys.org
  • #2
niyati said:
The coordinates of an object moving in the xy plane vary with time according to the equations x = -(5.00 m)sin(wt) and y = (4.00 m) - (5.00 m)cos(wt), where w is a constant and t is in seconds. (a) Determine the components of velocity and components of acceleration at t = 0. (b) Write expressions for the position vector, the velocity vector, and the acceleration vector at any time t > 0. (c) Describe the path of the object in an xy plot.

(a) When time is zero, the positions of x and y are 0 and 4, respectively. I am wondering how I can determine a velocity of a vertical line. I don't think it is zero, as that would be a horizontal line, and to have no slope would mean that there isn't a velocity. Where there is no velocity, there is no acceleration, so to find the components would be impossible.

(b) My problem here is that there are two different equations dealing with the components. It is not an independent variable as x and the dependent variable as y. However, if I squared both equations, added them, and then took the square root (like find the length of the hypotenuse), would that be an equation for the position? And since it says at any time greater than zero, am I to take the derivative of such equation to get the velocity, and again for the acceleration?

(c) I...really don't know what to do with this part, but I'm positive that this has something to do with part (b) (...duh), which, well, I'm not getting either.

I think I'm over-complicating things, especially in part (b), because nothing in this portion of my chapter (...the beginning) did anything this weird.

Help?

[tex]{a}_{x}=\frac{d}{d\,t}\,{v}_{x}[/tex]
[tex]{v}_{x}=\frac{d}{d\,t}\,{s}_{x}[/tex]
[tex]{v}_{y}=\frac{d}{d\,t}\,{s}_{y}[/tex]
[tex]{a}_{y}=\frac{d}{d\,t}\,{v}_{y}[/tex]

b) it's asking for the position vector...
and so use those parametric equations.


c) I would say it has nothing to do with b.
just eliminate t, and combine those two equations so as to make y>>x
 
Last edited:
  • #3
I have a big problem here, i don't understand a word, can someone explain it from the beginning ?
 
  • #4
SocratesOscar said:
I have a big problem here, i don't understand a word, can someone explain it from the beginning ?

What you don't understand?

This is a textbook problem. Start from your book definitions (or read rootx reply) of velocity, and acceleration. Remember that because this is a 2D movement, your vectors must account for both x and y components.
 

1. What are position vectors, velocity vectors, and acceleration vectors?

Position vectors, velocity vectors, and acceleration vectors are mathematical representations of the location, speed, and change in speed of an object at a specific point in time, respectively. They are typically represented by arrows, with the direction and magnitude of the arrow representing the direction and magnitude of the vector.

2. How are position vectors, velocity vectors, and acceleration vectors related?

Position vectors are the starting point for velocity vectors, which in turn are the starting point for acceleration vectors. In other words, velocity vectors are the derivatives of position vectors, and acceleration vectors are the derivatives of velocity vectors.

3. How do position vectors, velocity vectors, and acceleration vectors help in understanding motion?

Position vectors, velocity vectors, and acceleration vectors provide a quantitative way to describe the motion of an object. They allow us to calculate the position, speed, and change in speed of an object at any given time, and to analyze how these quantities change over time.

4. Can you give an example of how to use position vectors, velocity vectors, and acceleration vectors?

Sure! Let's say we have a car moving along a straight road. The position vector at any given time would tell us the location of the car on the road. The velocity vector would tell us the car's speed and direction of motion, while the acceleration vector would tell us how the car's speed is changing, for example if it is accelerating or decelerating.

5. What is the difference between velocity vectors and acceleration vectors?

The main difference between velocity vectors and acceleration vectors is that velocity vectors describe an object's speed and direction of motion, while acceleration vectors describe how an object's speed is changing. Velocity vectors have units of distance over time, while acceleration vectors have units of distance over time squared.

Similar threads

Replies
12
Views
566
  • Introductory Physics Homework Help
Replies
2
Views
776
Replies
5
Views
725
  • Introductory Physics Homework Help
2
Replies
38
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
690
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
774
  • Introductory Physics Homework Help
Replies
19
Views
825
Back
Top