The motion of a particle moving in a circle in the x-y plane is described by the equations: r(t)=8.27, Θ(t)=8.58t(adsbygoogle = window.adsbygoogle || []).push({});

Where Θ is the polar angle measured counter-clockwise from the + x-axis in radians, and r is the distance from the origin in m.

a)Calculate the y-coordinate of the particle at the time 1.60 s.

b)Calculate the x-component of the velocity at the time 1.90 s?

c)Calculate the magnitude of the acceleration of the particle at the time 3.70 s?

d)Calculate the x-component of the acceleration at the time 3.80s?

My teacher gave us a key to solve these but i can't make sense of it.

Part A

y = r(t)*sin(Θ(t)*t)

Part B:

vx = Θ*r*cos(Θ(t))

Part C:

ax= -(Θ^2)*r cos (Θ(t))

ay = -(Θ^2)*r sin (Θ(t))

a = sqrt(ax^2 + ay^2)

Part D:

ay = -(Θ^2)*r*sin(Θ(t))

I'm not sure what the difference is between Θ and Θ(t) & r and r(t)

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# Motion of a particle

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