March 28, 2017

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A particle travels counterclockwise around the origin at constant speed in a circular path that has a diameter of 2.50 m, going around twice per second. Point Q is on the path halfway between points P and R, which lie on the x axis and the y axis, respectively. State the following velocites as vectors in polar notation. (a) What is the particle's average velocity over the interval PR? (b) What is its average velocity over the interval PQ? (c) What is its instantaneous velocity at point P?

Point P is at coordinates (1.25,0) and point R is at coordinates (0,1.25). Point Q is directly in the middle of P and R. Can you explain the answers as well so I understand?!

Part C starts with (15.7, ? degrees)
That's all I know.


    Linear velocity is v = ω•R=2•π•n•R =2•π•2•1.25 =15.7 m/s.
    The quarter of the circle is covered for the time
    t = 2•π•R/4•2•π•n•R =1/8 s =0.125 s.
    Displacement for this time is the distance betwee point P and Q
    D =sqrt(R² +R²) 1.25•1.41 = 1.76m.
    v(ave) =displacement/ time =
    1.76/0.125 =14.1 m/s.
    Time for covering the 1/8 part of circle is
    t =1/16 =0.0625 s.
    Displacement (using cosine law) is
    D =sqrt(R² +R² -2 R²cos45º)=0.96 m
    v (ave) = 0.96/0.0625 =15.3.
    Instanteneous linear velocity is
    v = ω•R=2•π•n•R =2•π•2•1.25 =15.7 m/s.

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