The position vector for a particle moving on a helix is c(t)= (cost, sint, t^2). Find the speed of the particle at time t = 4pi

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24-11-2016
Physics

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The position vector for a particle moving on a helix is c(t)= (cost, sint, t^2). Find the speed of the particle at time t = 4pi

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scme1702 scme1702 · Answer 1 · 2016-11-27T16:58:12+01:00

scme1702 scme1702

27-11-2016

We differentiate the position vector to obtain the velocity vector:
v(t) = (-sin(t), cos(t), 2t)
Now, substituting 4π
v(t) = 0, 1, 8π

We calculate the magnitude of the velocity to obtain the speed:
s = √(0² + 1² + (8π)²)
s = 25.2

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