Isn't a constant?
Hi there,
I have a particle traveling on a curve defined by (x,y) = r(t) where r(t) = (cos t, sin t, t)
I know this is a helix with the image being a circle, and I need to prove that the particle travels at a constant speed. I know grad r(t) will give me the tangent vector at a point ie (-sin t, cos t, 1). I thought that since grad gives rate of change, then a magnitude of 0 would mean constant speed. So trying this:
grad (cos t, sin t, t) = (-sin t, cos t, 1) and || (-sin t, cos t, 1)|| = root(2)..
meaning its not a constant speed right? But i know i'm wrong because my problem asks me to prove the speed is constant. CAn anyone advise please?
Thanks!
Hello, iva!
A particle travels on a curve defined by: , where: .
I know this is a helix with the image being a circle,
and I need to prove that the particle travels at a constant speed.
I know. gives me the tangent vector at a point, i.e.
I thought that since gives rate of change,
then a magnitude of 0 would mean constant speed. . no!
is the velocity of the particle.
. . It provides the direction and the speed of the particle.
The speed is the magnitude of the velocity: .
. . Hence: .
At any time , the speed is units/second.
. . The speed is constant.