How does exposure time affect motion blur in photography?

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Suppose we want to take a picture of a highway at night, see attachments.

As far as i understood, whether image is freezed or with this blured moving effect determines by the shutter speed. Short exposure time corresponds to freezed picture, long expisure time to motion effect.

I don't understand how the expossure time corresponds to final image. Image sensor get sampled multiple times and then avarage result delivers as a final picture? If so, then how the motion blur effect is done in analog cameras.

Or image sensor get sampled only once? In this case all images suppose to be freezed images, as you sample the particular current on photodiodes at the particular time of sampling.
 
Attachments
  • Long-exposure night photo of a multi-lane highway, with streaks of white and red light from moving headlights and taillights, and street lamps and traffic signals along the road.
    400px-E17_-_lange_sluitertijd.JPG
    19.6 KB · Views: 532
  • Night photograph of a multi-lane highway with light trails from moving headlights and taillights, overhead street lamps, and green gantry signal lights above the lanes.
    400px-E17_-_korte_sluitertijd.JPG
    17.1 KB · Views: 544
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Discussion

The sensor is only sampled once. The "shutter speed" on a digital camera is equivalent to that on a film camera: the sensor collects photons for the pre-determined time, then then the result is read.