Answer:
[tex]K=\frac{2}{(4t^{2}+1)^{\frac{3}{2}}}[/tex]
Step-by-step explanation:
First of all, we calculate v and a as:
[tex]v(t)=\frac{dr(t)}{dt}=(2t,1,0)[/tex]
[tex]a(t)=\frac{dv(t)}{dt}=(2,0,0)[/tex]
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
[tex]| v |^{3} = (4t^{2}+1)^{\frac{3}{2}}[/tex]
Hence we have
[tex]K=\frac{2}{(4t^{2}+1)^{\frac{3}{2}}}[/tex]
I hope this is useful for you
regards
