Assume velocity is defined as v(t) = r (t) and acceleration as a(t) = r (t). Sup
ID: 2857308 • Letter: A
Question
Assume velocity is defined as v(t) = r (t) and acceleration as a(t) = r (t). Suppose a particle moves in circular motion descrived by r(t) = [45 cos(4t), 45 sin(4t)]. Select the true statement/s A. a(t) = [720 cos(4 t), 720 sin (4 t)]
B. ||a(t)|| = 4 · ||v(t)||
C. a(t) = 4 2 · r(t)
D. v(t) = [180 sin (4 t), 180 cos(4 t)]
E. ||a(t)|| = 42 · 45
F. a(t) · v(t) = v (t) · v(t) = 1 2 (v(t) · v(t))
G. 1 2 (v(t) · v(t)) = 1 2 ( ||v(t)||2 ) = 1 2 ( [45 · 4]2 )
H. a(t) · v(t) = 0
I. a(t) v(t) for every value of t
Explanation / Answer
Use chain rule of derivative
So v(t) = r'(t) = ( -180 sin(4t) , 180 cos(4t) )
a(t) = v'(t) = ( -720 cos(4t) , -720 sin(4t) )
So a(t) = - 4* v(t)
So choice A , B , C , H and I are correct.