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.
 

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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.