Physics Practice Problems Motion in 2D & 3D With Calc Practice Problems Solution: Cycloid. A particle moves in the xy-plane. Its co...

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Solution: 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 omega 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?

Problem

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?