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I am given the position $r(t)$ at time $t$ of a particle moving in space and need to find its direction at a given time, but I don't exactly know how to do it. At first I thought the direction was the curvature but it seems I'm wrong.

How can I find the direction of the particle?

UPDATE: Specifically the question is: The position of a particle moving in space at time $t$ is $r(t) = \dots$. Find the direction of the particle at time $t$ and write the velocity of the particle at any time as the product of its speed and its direction.

Camile Delmas
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  • Are you given an equation of some type for the particle's position? – recursive recursion Feb 09 '14 at 23:27
  • If I understand your question right, the direction of the particle is the same as the direction of its velocity vector, which is $\frac{dr(t)}{dt}$. – TonyK Feb 09 '14 at 23:28
  • @recursiverecursion Yes, I have it but decided not to write it 'cause I want to solve the problem myself, just don't know what to do ;-) – Camile Delmas Feb 09 '14 at 23:30

2 Answers2

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The direction is $\frac{r'(t)}{|r'(t)|}$ and and the velocity is $r'(t)$

Semsem
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If the particle is at $\vec r(t)$ at $t$, and at $\vec r(t+dt)=\vec r(t)+\vec r'(t)\ dt$ at $t+dt$, then it has moved in the direction of $\vec r'(t)$.

A unit vector in this direction is

$$\vec t(t)=\frac{\vec r'(t)}{\|\vec r'(t)\|}.$$