Motion of a Particle in a Plane: A Quiz

[lobbob]

Homework Statement

If a particle moves in a plane so that its position is described by the functions
x=Acosωt, and y= Asinωt, it is
(A) moving with varying speed along a circle
(B) moving with constant speed along a circle
(C) moving with constant acceleration along a straight line
(D) moving along a parabola
(E) oscillating back and forth along a straight line

Homework Equations

None

The Attempt at a Solution

Don't understand the problem. I just need to know how to start it.

 

[Nathanael]

Homework Statement

If a particle moves in a plane so that its position is described by the functions
x=Acosωt, and y= Asinωt, it is
(A) moving with varying speed along a circle
(B) moving with constant speed along a circle
(C) moving with constant acceleration along a straight line
(D) moving along a parabola
(E) oscillating back and forth along a straight line

Homework Equations

None

The Attempt at a Solution

Don't understand the problem. I just need to know how to start it.

Those two functions describe the x coordinate and the y coordinate at any (and every) time "t"

What path do you think the particle will move along and why?
(In other words, what are all the possible (x,y) coordinates for all the times "t"?)

 

[NascentOxygen]

Don't understand the problem. I just need to know how to start it.

You probably won't succeed in answering this confidently without an understanding of SHM, as the question basically is testing your knowledge of the topic.

A good place to start might be here: http://en.wikipedia.org/wiki/Simple_harmonic_motion

 

[tms]

Homework Statement

If a particle moves in a plane so that its position is described by the functions
x=Acosωt, and y= Asinωt, it is
(A) moving with varying speed along a circle
(B) moving with constant speed along a circle
(C) moving with constant acceleration along a straight line
(D) moving along a parabola
(E) oscillating back and forth along a straight line

Homework Equations

None

The Attempt at a Solution

Don't understand the problem. I just need to know how to start it.

Just plug in a few sample values and see what you get. Where is the particle when $\omega t$ is 0? When it is $\pi / 2$? When $\pi$? When $2 \pi$?

 

[HalfLostAndSearching]

I would first clarify the problem by defining the variables and terms used. In this case, x and y represent the position of the particle in the plane, A is the amplitude of the motion, ω is the angular frequency, and t is time. The options given represent different types of motion that the particle could be undergoing based on these equations.

To start solving this problem, I would use the equations of motion to analyze the particle's position, velocity, and acceleration. From the given equations, we can see that the particle is undergoing circular motion, as both x and y are functions of the same trigonometric function with the same frequency ω. This means that the particle is moving in a circle with a radius of A.

Next, we can look at the particle's velocity, which is given by the first derivative of its position equations. We can see that the particle's speed is constant, as it is not changing with time. This eliminates options (A) and (E), as both of these options involve varying speed.

Finally, we can look at the particle's acceleration, which is given by the second derivative of its position equations. We can see that the particle's acceleration is constant and directed towards the center of the circle, as it is always perpendicular to the velocity. This means that the particle is undergoing uniform circular motion, and is therefore moving with constant acceleration along a circular path. This eliminates options (C) and (D).

Therefore, the correct answer is option (B) - the particle is moving with constant speed along a circle.