Aparticle moves along a circular path over a horizontal xy coordinate system, at constant speed. at time t1 = 4.50 s, it is at point (5.80 m, 5.60 m) with velocity (3.50 m/s) j and acceleration in the positive x direction. at time t2 = 11.7 s, it has velocity (–3.50 m/s) 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.

a) x=11.15m

b) y= 5.6m

Explanation:

This is the given data:

t1=4.5s                          t2=11.7s

V1=3.5 (j)m/s                 V2=-3.5 (i)m/s

a1 = a(i)                          a2 = a(j)

r1 = 5.8(i)+5.6(j) m

From this data we conclude that the orbit is as the one shown in the picture.

So, the position of the center will be rc = r1 + R(i) = (5.8+R)(i) + 5.6(j)

Calculating the distance traveled by the particle:

S = V*Δt = 3.5 * (11.7-4.5) = 25.2m

Since S = θ * R  and from the picture we know that θ = 3π/2

R = 5.35m

Now we calculate the center of the orbit as:

rc = r1 + R(i) = (5.8+5.35)(i)  +  5.6(j) = [11.15(i) + 5.6(j)] m

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.