# Physics

posted by .

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?

P coordinates: (1.25, 0)
R coordinates: (0, 1.25)
Q is directly between the two

• Physics -

frequency f = 2 rev/s
angular velocity = 2•π•f = 4•π rad/s
(a) Velocity vector at P = (1.25x4x3.14)j = 15.7 j,
where j is unit vector along positive y axis.
Also velocity vector of the particle at R = -15.7i,
where i is unit vector along positive x direction.
As the direction changes uniformly,
the average velocity over the interval PR is
(15.7/2)(j-i)= 7.85(j-i).
Magnitude = sqrt[7.85^2+7.85^2] =
=1.414x7.85 = 11.10 m/s
and the direction is 45 degrees west of north.
(b) Average velocity, V1 over interval PQ is
= 0.5{15.7 j + [15.7/sqrt(2)](j-i)} or
V1 = 0.5[26.80 j - 11.10i] = 13.40 j - 5.55 i.
Magnitude of V1 = sqrt[13.40^2 + 5.55^2] = 14.50 m/s.
due theta west of north given by theta = tan^-1 [5.55/13.40] = 22.5 degrees west of north.
(c) v= 2•π•f•R = 15.7 m/s due north

## Similar Questions

1. ### Math

A circular path around a lake has a diameter of 2,000 feet (ft). Pranotti jogs around the path 5 times for her morning run. How far does she run?
2. ### Physics

(a)A car travels exactly once around a circle of radius 5.0 m at constant speed of 3.0 m/s. What is the car’s average velocity (magnitude and direction) during this interval?
3. ### physics

A particle with a charge 7C and a mass of 20kg is traveling in a circular path around a fixed particle of charde -5C. The velocity is observed to be 3000m/sec. What is the radius of the circular path?
4. ### Physics

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 …

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 …
6. ### Physics

Which of the following is not a good example of uniform circular motion?
7. ### calculus

a particle is moving counterclockwise around the circular path whose equation is x^2+y^2=100 of the abscissa of the particle is increasing by 72in/sec at a point where x=8 find the rate of changeof the cordinate(y) at this point
8. ### Geometry

A scientist is plotting the circular path of a particle on a coordinate plane for a lab experiment. The scientist knows the path is a perfect circle and that the particle starts at ordered pair (-5, -11). When the particle is halfway …
9. ### Pre Calculus

A park has a circular walking path with a diameter of 250 meters. a) Write the equation to describe the walking path in your diagram. b) Find the distance traveled by someone walking once around the entire path. c) Find the distance …
10. ### physics

a woman walks along a circular path of radius of 15m it takes her 2min to get halfway around the path at this halfway point what is her approximate distance traveled, displacement, average speed in m/s, and average velocity in m/s?

More Similar Questions
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.jiskha.com/display.cgi?id=1337972192", "fetch_time": 1516483523000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-05/segments/1516084889733.57/warc/CC-MAIN-20180120201828-20180120221828-00083.warc.gz", "warc_record_offset": 922428101, "warc_record_length": 4438, "token_count": 985, "char_count": 3588, "score": 3.859375, "int_score": 4, "crawl": "CC-MAIN-2018-05", "snapshot_type": "latest", "language": "en", "language_score": 0.9054409861564636, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00024-of-00064.parquet"}