Question

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

Answer 1

i do need the practice

Answer 2

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

Answer 3

lol....

Answer 4

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

Answer 5

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