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[SOLVED] Velocity and acceleration

Dhamnekar Winod

Active member
Nov 17, 2018
163
A particle moves so that its position vector is given by $\vec{r}=\cos{(\omega t)}\hat{i} + \sin{(\omega t)}\hat{j}$. Show that the velocity $\vec{v}$ of the particle is perpendicular to $\vec{r}$ and $\vec{r} \times \vec{v}$ is a constant vector.

How to answer this question?
 
Last edited:

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,274
First calculate \(\displaystyle \vec{v} = \dfrac{d \vec{r}}{dt}\). If \(\displaystyle \vec{r} \cdot \vec{v} = 0\) for all t then they are always perpendicular.

-Dan
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
821
Since the velocity function is the derivative of the position function and the acceleration function is the derivative of the velocity function, I would say, "start by taking a Calculus class!". Have you done that? Do you know what the derivatives of $cos(\omega t)$ and $sin(\omega t)$ are? Do you know how to show that one vector is perpendicular to another? (Dot product.)