Question

Find the speed of a particle at time t = 8 whose position vector is vector r equals cosine times pi over 4 times t, 2 times sine of pi over 4 times t . (15 points)

A) 0
B) pi over 2
C) π
D) 3 times pi over 2

Answer 1

I guess you mean R = cos (pi t/4) i + 2 sin pi t/4 j
dR/dt = - (pi/4) sin ( pi t/4) i + (pi/2) cos (pi t/4)j
when t = 8
dR/dt = - pi/4 * 0 i + (pi/2) cos 2 pi j
cos 2 pi = -1
so dR/dt vector = 0 i - pi/2 j
|dR/dt| = speed = pi/2
B