Uniform circular motion of a particle problem

[J-dizzal]

Homework Statement

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.

Homework Equations

a=v²/r, v=2πr/T, [/B]

The Attempt at a Solution

 

[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.

 

[J-dizzal]

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.

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?

 

[tony873004]

Is it given that its moving clockwise?

 

[J-dizzal]

Is it given that its moving clockwise?

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

 

[tony873004]

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