Question

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

Answer 1

Answer:

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

Step-by-step explanation:

First of all, we calculate v and a as:

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

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

after that, we compute the cross product and we replace in the formula for k

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

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

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

Hence we have

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

I hope this is useful for you

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