How do you find the distance travelled from 0<=t<=1 by an object whose motion is x=e^tcost, y=e^tsint?

1 Answer
May 9, 2018

sqrt 2 \ (e - 1)

Explanation:

Let z(t) = x(t) + i \ y(t) = e^((1+i)t)

dot z = (1+i) e^((1+i)t)

Speed (not velocity) is needed to calculate distance s:

s = int_0^1 sqrt (abs(dotz)^2) \ dt

abs(dotz)^2 = dot z bar (dot z)

= (1+i) e^((1+i)t) * (1-i) e^((1-i)t) = 2 e^(2t)

implies s =sqrt 2 int_0^1 e^(t) \ dt = sqrt 2 \ (e - 1)