# Motion of a particle given position vector.

1. May 6, 2012

### tcanman

1. The problem statement, all variables and given/known data

A position vector of a particle at a time t is r=icost +jsint +kt ; show the speed and the magnitude of the acceleration is constant. Describe the motion.

2. Relevant equations

v = dr/dt
a = dv/dt

3. The attempt at a solution

Could someone let me know if I am doing this correctly?

I derived the position to find the velocity:

v = dr/dt = -isint +jcost + 1k

Then derived the velocity :

a = dv/dt = -icost -jsint

Then found the magnitude of the acceleration:

mag(a) = sqrt ( cos^2(t) + sin^2(t)) = 1 , which is constant.

Motion- increasing oscillation? How would I show this?

Thanks!

2. May 6, 2012

### Steely Dan

Don't forget to find the speed (magnitude of the velocity).

Think about just the two-dimensional $x,y$ motion. What kind of motion would that be? Then notice that the $z$ component just linearly increases in one direction. What kind of shape will be created this way? And how will your particle move along that three dimensional shape?

3. May 6, 2012

### tcanman

I took the magnitude of the velocity and got sqrt( sin^2 + cos^2 +1) so sqrt(2) , so it would also be constant.
Would the particle just be moving around a circle? How could I prove this?

Thanks!

4. May 6, 2012

### Steely Dan

Well, yes for the two-dimensional case it would be circular motion. If you don't recognize the form, try picking various values of $t$ and plotting them on a two dimensional graph to see it.

5. May 6, 2012

### tcanman

Is it supposed to look like a spring? And was I correct about the velocity?

Thank you for the help.

6. May 6, 2012

### Steely Dan

Exactly, it's the shape of a helix. The motion is circular, but it's traveling upwards along the surface of a cylinder with time.

And yes, you were right about the speed.

7. May 6, 2012

### tcanman

Awesome! Thanks!

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