What you are seeing here is most likely motion blur.
Either you turn motion blur off globally (in the post process settings), or you try to generate motion vectors for your static mesh. To check if the motion vectors really are the issue, you can enable the MotionBlur visualization and check if you are getting any motion vectors from your attached static mesh.
Then you can try creating the motion blur manually. For example by feeding the OwnerVelocity into the motion blur. Here is a post as to how to set motion blur manually on particles: