Use the alternative curvature formula K=|a x v|/|v|^3 to find the curvature of the following parameterized curves.

Mathematics

1 answer:

PIT_PIT [12.4K]2 months ago

8 0

Answer:

$K=\frac{2}{(4t^{2}+1)^{\frac{3}{2}}}$

Step-by-step explanation:

First, we determine v and a as:

$v(t)=\frac{dr(t)}{dt}=(2t,1,0)$

$a(t)=\frac{dv(t)}{dt}=(2,0,0)$

Subsequently, we compute the cross product and substitute it into the formula for k

a(t) X v(t) = (0,0,2)

| a(t) X v(t) | = 2

$| v |^{3} = (4t^{2}+1)^{\frac{3}{2}}$

Thus, we conclude

$K=\frac{2}{(4t^{2}+1)^{\frac{3}{2}}}$

I trust this is of assistance to you

best regards

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