** Cycloid.** A particle moves in the xy-plane. Its coordinates are given as functions of time by

x( t ) = R(t-sint)y( t ) = R(1-t)

where R and are constants.

Determine the velocity x-component of the particle at any time t.

At which times is the particle momentarily at rest?

Does the magnitude of the acceleration depend on time?

Determine the velocity y-component of the particle at any time t.

Determine the acceleration x-component of the particle at any time t.

Determine the acceleration y-component of the particle at any time t.

What is the x-coordinate of the particle at these times?

What is the magnitude of the acceleration at these times?

What is the y-coordinate of the particle at these times?

What is the direction of the acceleration at these times?

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