Provide an Appropriate Response $r ( t ) = t ^ { 5 } i + t ^ { 3 } j$

Multiple Choice

Provide an appropriate response.
-The following equations each describe the motion of a particle. For which path is the particle's velocity vector alv orthogonal to its acceleration vector?
(1) $r ( t ) = t ^ { 5 } i + t ^ { 3 } j$
(2) $r ( t ) = \cos ( 10 t ) \mathbf { i } + \sin ( 9 t ) \mathbf { j }$
(3) $r ( t ) = t i + t ^ { 3 } j$
(4) $r ( t ) = \cos ( 4 t ) i + \sin ( 4 t ) j$

A) Path (2) and Path (4)
B) Path (4)
C) Path (3)
D) Path (1)