A moving particle has a position vector r(t)= a) is r(t) defined in the interval [0,2]? If not, where is r(t) defined in this interval?

A moving particle has a position vector r(t)= <-sin x, ln(cos x), cos x>

a) is r(t) defined in the interval [0,2]? If not, where is r(t) defined in this interval? (Note: make sure you indicate whether the endpoints are included)

b) Calculate the instantaneous velocity and acceleration of this moving particle at time t.

c) What is the distance this moving particle has traveled between t=0 and t=/4? (Hint: The particle is traveling on the curve defined by the vector funtion. So the distance traveled is the length of a segment of the curve.)

d) What is its average speed over the time interval t=0 to t=/4?