Speed is relative.  The car is travelling at 40mph relative to the Earth's surface, but at 0mph relative to the driver - otherwise the driver would not be in the seat for very long.  In an accident, the car's speed changes before the driver's does - that's why you get whiplash, or thrown into the steering wheel.

Similarly, we have no 'real' speed in the universe.  The galaxy is in motion relative to other galaxies, but we are moving towards some and away from others.  The relative speed depends on where you're measuring from.  Certainly the relative speed could be large enough that relativistic effects, such as time dilation, are visible.