# Velocity of a moving particle

1. Homework Statement

A particle moves down with position vector <sec(Pi*t), tan(Pi*t)> for
0 =< t < 1/2.

(a). Find the velocity and speed of the particle at t = 1/4.
(b). The particle movies along a hyperbola. Elminate the parameter to find an equation of the hyperbola in terms of x and y.
(c). Sketch the path of the particle over the time interval
0 =< t < 1/2.

2. Homework Equations

? none?

3. The Attempt at a Solution

velocity vector = < Pi*sec(Pi*t)tan(Pi*t), Pi*sec^2(Pi*t)>
Plug in 1/4 into velocity vector:
<.04307, Pi>

Question is (part a), it's asking for velocity. I'm thinking writting velocity vector isn't the same thing; should I do a pythagorean theorem on the two components of my velocity vector to get a single value for velocity?

Help appreciated :P

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I think you're confusing speed and velocity. Velocity is a vector, speed is not. So, the form you currently have the velocity in is sufficient. If you find the magnitude (i.e. what you call "doing a pythagorean theorem"), you'll have to also specify a direction, which is much more work than you need.

Phew...so I just pull pythagorean for speed?

yup.

Sweet! Thanks :)