Question

Find the speed of an object with r(t)=e^(t).

Answer 1

\[v(t)=e ^{t}<\cos t-\sin t, \cos t+\sin t, 1>\]

Answer 2

How do I find \[\left| v(t) \right|\]?

Answer 3

@thomaster @amistre64

Answer 4

take the derivative ...

Answer 5

x(t) = e^t cos(t)
y(t) = e^t sin(t)
z(t) = e^t


x'(t) = e^t cos(t) - e^t sin(t)
y'(t) = e^t sin(t) + e^t cos(t)
z'(t) = e^t

Answer 6

how do you find the length of a vector?

Answer 7

sqrt(u.u)

Answer 8

(x')^2 = e^(2t) (cos(t) - sin(t))^2

(y')^2 = e^(2t) (sin(t) +cos(t) )^2

(z')^2 = e^(2t)
-------------------------

(x')^2 = e^(2t) (cos^2(t) +sin^2(t) - 2sin(t)cos(t))

(y')^2 = e^(2t) (cos^2(t) +sin^2(t) +2sin(t)cos(t))

(z')^2 = e^(2t)
---------------------------

e^(2t) (1+1-2sc+2sc+1)

3e^(2t)
----------------------

etc ....

Answer 9

How did you get e^(2t)(1+1-2sc+2sc+1) and 3e^(2t)?

Answer 10

thats all written up there ...

Answer 11

for a vector u in R^n the length |u| is determined as:
\[|u|=\sqrt{x_1^2+x_2^2+x_3^2+...+x_n^2}\]

Answer 12

Oh, I see. So the sqrt(3e^(2t))=sqrt(3)*e^t, which is the answer, right?

Answer 13

thats what i come up with if memory serves yes

Answer 14

Thank you! :)

Answer 15

youre welcome