Warp travel in Star Trek is not faster than light. The warp drive just “shortens” the distance and the impulse drive pushes the ship through the shorter distance. That’s why its called warp drive and not FTL drive. (sources: Mr Scott’s Guide To The Enterprise and the Star Trek: The Next Generation Technical Manual)
Spin Dizzies from “Cities in Flight”.
I thought the Enterprise was stationary inside a moving warp bubble.