Question

A particles position as a function of time is given by u = cos 2t i+sin 2t j ( The u, i and j should have tilde's underneath as they are vectors)

(a) find the equation of the path

Answer 1

x = cos(2t)
y = sin(2t)
z = 0

Answer 2

thats not the answer i sorta know how to do it but the 2t throws me off abit

Answer 3

thats the equation of a line in R^3 :) well, except for an initial point

Answer 4

the position path just produces a unit circle

Answer 5

yes i understand that but normally you would eliminiate the sin and cos by squaring x and y then adding them

Answer 6

im not sure what happens to the 2t

Answer 7

2t just modifies the speed of rotation; nothing more

Answer 8

its going twice as fast around the unit circle

Answer 9

i see so the working is like this;

x = cos 2t
y=sin2t

x^2=cos^2t
y^2=sin^2t

x^2+y^2=1

i ignore the 2t correct

Answer 10

or simply redefine it; 2t = u

Answer 11

it has no importance on position; other than it a given t it is at this location; but the path remains unchaged by it

Answer 12

tell me; does a person walking along the sidewalk get to the same place as the person jogging on the sidewalk?

Answer 13

yes thats correct. thanks so much you actually made me understand the question.

Answer 14

youre welcome :)