Posted by **Rachel** on Friday, May 25, 2012 at 2:56pm.

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 -
**Elena**, Friday, May 25, 2012 at 3:18pm
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

## Answer this Question

## Related Questions

- PHYSICS PLEASE HELP - A particle travels counterclockwise around the origin at ...
- Physics - A particle travels counterclockwise around the origin at constant ...
- Geometry - A scientist is plotting the circular path of a particle on a ...
- Pre Calculus - A park has a circular walking path with a diameter of 250 meters...
- Physics - (a)A car travels exactly once around a circle of radius 5.0 m at ...
- calculus - a particle is moving counterclockwise around the circular path whose ...
- physics - A particle with a charge 7C and a mass of 20kg is traveling in a ...
- Physics - Which of the following is not a good example of uniform circular ...
- Math - A circular path around a lake has a diameter of 2,000 feet (ft). Pranotti...
- math - Find the distance that the earth travels in seven days in its path around...

More Related Questions