If r(t)=−4ti+4t2j+2tk, compute the tangential and normal components of the acceleration vector.

Question

amistre64 · Answer

i do need the practice

anonymous · Answer

Well practice on.  If you get it by 9:45 I can tell you if you are correct

amistre64 · Answer

lol....

amistre64 · Answer

have to be able to get the site to run to right on my computer tho

amistre64 · Answer

$$ r(t)=<−4t,4t^2,2t>$$ $$ r'(t)=<−4,8t,2>$$ $$ |r'(t)|=\sqrt{16+64t^2+4}$$ $$ r''(t)=<0,8,0>$$ $$ r'.r''=<−4,8t,2>.<0,8,0>=64t$$ $$ r'(x)r''=<−4,8t,2>(x)<0,8,0>=<-16,0,-32>$$ $$ |r'(x)r''|=\sqrt{16^2+32^2}$$ $$a_t=\frac{r'.r''}{|r'|}=\frac{64t}{\sqrt{20+64t^2}}$$ $$a_n=\frac{|r'(x)r''|}{|r'|}=\frac{\sqrt{16^2+32^2}}{\sqrt{20+64t^2}}$$