Question

Calc 3 problem

a particle moves so its position vector at time t is r(t) = (1/t)i+t^2j+t^3k. find scalar tangential and normal components of acceleration at time t = 1.

Appreciate all the help I can get

Answer 1

ok. we need vector acceleration equation of the particle. differentiate twice.

Answer 2

\[\vec{v}=(-1/t^2)i+2t j + 3t^2k\]

Answer 3

a = 2/t^3i+2j+6tk?

Answer 4

yeah

Answer 5

now you have to decompose the vector:\[\vec{a}(1)=<2,2,6>\] into tangential and normal components

Answer 6

start with the tangential component. if we take the acceleration vector and dot product it with the unit tangent vector, this should give us the tangential component of the acceleration. ditto for the normal component using the unit normal vector.

Answer 7

In fact:\[\vec{a}=a_{T}*\hat{T}+a_{N}\hat{N}\]

Answer 8

sorry, missed the dot product sign above. a_{N}*N

Answer 9

what is the unit tangent vector when t=1?

Answer 10

uhhh, looking through my notes now for the subject

Answer 11

teacher doesn't use a book, and only gives us lecture notes and examples he comes up with. so looking through my whole notebook of notes at the moment xP

Answer 12

how about any vector tangent to the curve r(t)?

Answer 13

just the derivative of the orignal function?

Answer 14

yep. the velocity vector