7 consider the curve produced by the vector valued function f t 4t 3co

Question

7. Consider the curve produced by the vector valued function, F(t)=(4t, 3cost, 3sint), which represents
the position of particle in space at time t.
(5 points)
Determine the arc length of the curve over the interval 0st<
t</2.
b) Re-parameterize the curve in terms of its arc length s.
c) Determine the position of the particle after it has traveled a distance of 57 units.