A particle P travels with constant speed on a circle of radius r = 4.0 m (see th

Question

A particle P travels with constant speed on a circle of radius r = 4.0 m (see the figure) and completes one revolution in 20.0 s. The particle passes through 0 at t = 0.

For the 5.00 s interval from the end of the fifth second to the end of the tenth second, find the particle's average velocity. What is the x and y component of the average velocity?

Find its velocity at the beginning and end of that 5.00 s interval. What is the x and y-component of the velocity at t= 5.0 s?

Find its acceleration at t = 5.0 s? What is the x and y-component of the acceleration at t = 5.0 s?

ind its velocity at the end of that 5.00 s interval. What is the x and y-component of the velocity at t = 10.0 s?

Find its acceleration at t = 10.0 s? What is the x and y-component of the acceleration at t = 10.0 s?

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Explanation / Answer

The speed of the particle is

v = 2 pi r / T = 1.2566 m/s

At 5 to 10 s, it is on the rightmost to the topmost.

Thus, the average velocity is the velocity at the upper right,

vave = 1.2566 m/s, to the upper left.   [ANSWER]

***********************

Beginning: 1.2566 m/s, upward
End: 1.2566 m/s, to the left

************************

At 5 s,

ac = v^2/R

Thus,

ac = 0.3948 m/s^2, to the left [ANSWER]

*********************

At 5 s,

ac = v^2/R

Thus,

ac = 0.3948 m/s^2, downward [ANSWER]

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