# Find the velocity vector for the particle at any time

1. Apr 25, 2004

### Tiki

During the time period t=0 to t=6 seconds, a particle moves along the path given by x(t)=3cos(pi*t) and y(t)=5sin(pi*t)

1. Find the velocity vector for the particle at any time t.
2. Write and evaluate an integral expression, in terms of sine and cosine, that gives distance the particle travels from time t=1.25 to t=1.75.

Not quite sure what a velocity vector is...

For the second, it looks like an arclength so it would be Integral from 1.25 to 1.75 Sqrt((dy/dt)2 + (dx/dt)^2), so just derive the given (3cos(pi*t), etc. and plug in?

2. Apr 25, 2004

### arildno

1. Do you know the concept "position vector", and how positions are related to velocities?
2. That's right.

3. Apr 25, 2004

### Tiki

Does it have something to do with slope?

4. Apr 25, 2004

### arildno

The position vector gives the point in space where the particle is at a given time.
Since, in general, that point in space has three coordinates (x,y,z), the particle's position must be described with a vector quantity, not a single number.
Hope this helps..