Uniform circular motion of a particle problem

1. Jun 23, 2015

J-dizzal

1. The problem statement, all variables and given/known data
A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s)$\hat j$ and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity (–3.90 m/s)$/hat i$and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.

2. Relevant equations
a=v2/r, v=2πr/T,

3. The attempt at a solution

2. Jun 23, 2015

tony873004

If all its speed is in j-hat while at (5.1, 6.8), then it is crossing the horizontal axis through the circle at that moment. Hence, the y-component of the center is the y-component of (5.1,6.8)

It’s tangential speed is 3.9 m/s. It takes 9.9-3.3 seconds to travel ¼ around its orbit. (I’m assuming it didn’t go 5/4, or 9/4 around, etc.). So now you have a speed and a time, so you can solve for distance (circumference). Then it’s easy to get radius. If you know the radius and you know its position when all its velocity in is the j hat direction, then your radius is the offset from you x-component of that position.

3. Jun 23, 2015

J-dizzal

would'nt it travel 3/4 around the circle 3pi/2 if its velocity is positive jhat at the left side of the circle its moving clockwise?

4. Jun 23, 2015

tony873004

Is it given that its moving clockwise?

5. Jun 23, 2015

J-dizzal

no but both vectors are pointing in a direction that would indicate clockwise motion

6. Jun 23, 2015

tony873004

You're right, it moves 3/4 around.