Uniform Circular Motion of a particle

Im new at physics and have been looking at this question all day, any help would be greatly appreciated,

here it is

A particle moves along a cirular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.00s, it is at point (5.oom, 6.00m) with velocity (3.00 m/s)j and acceleration in the positive x direction. At time t2 = 10.0s, it has velocity (-3.00 m/s)i and acceleration in the positive y direction. What are the x and y coordinates of the centre of the circular path.

mezarashi
Homework Helper

1. The center of the circular motion

Draw out a diagram of a particle under circular motion. At each quarter circle, draw out the vectors for velocity and acceleration. Compare it to your questions problem.

The times give you a clue to finding the radius and subsequently the center of the motion. Within (10 - 4)seconds, the object moved from one part of the circle to another. You know d = vt. You also know that v^2/r defines acceleration in circular motion. A bit tricky, but I hope now you can start thinking about it.

thanks for the post, but i'm still lost????

mezarashi
Homework Helper

Draw out a diagram of a particle under circular motion. At each quarter circle, draw out the vectors for velocity and acceleration. Compare it to your questions problem.

from the diagram i see that at the first point its in the 2nd quarter and at the second point its in the 4th quarter( moving in a clockwise direction). Would the radius be the square root of (5^2 + 6^2). I still can't understand how this would relate to an xy centre coordinate(I thought the centre coordinate should be the origin of your plane).

mezarashi
Homework Helper
shawpeez said:
from the diagram i see that at the first point its in the 2nd quarter and at the second point its in the 4th quarter( moving in a clockwise direction). Would the radius be the square root of (5^2 + 6^2). I still can't understand how this would relate to an xy centre coordinate(I thought the centre coordinate should be the origin of your plane).

Aha, you're starting to understand a bit now. Your direction of motion is also correct. Not so fast about the radius just yet. You were drawing your own diagram based on the center of the motion being at 0,0. But in this case, the center isn't there, and you must find it. Can you find the corresponding point on the question's x-y coordinate for the first point? From there you can possibly estimate where the 2nd point would be, but you can't tell until you know the radius.

Now to finding this radius. You know that points 1 and 2 are separated by 3/4 of a circle, do you agree? Refer back to the diagram you drew. The circumference of a circle can be described as $$2\pi r$$. Now we know it took (10-4) seconds to make its way across three quarters of it, where d = vt. Getting closer?

HallsofIvy