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While experimenting with my 600d, I have noticed that on the same shutter speed, without inbuilt flash I get motion blur in my pictures, but with flash there is little to not motion blur (on the same shutter speed that produced motion blur without flash).

Why does this happen?

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Simple: the flash duration is very short. A full-powered flash is usually around ¹⁄₂₀₀th of a second, and if less than full power is used, it can be in the ¹⁄₁₀₀₀₀th range. If this flash is the only significant contributor of light in the image (and indoors, it's easy for that to be the case), the rest of the time the shutter is open just doesn't matter. That short pulse is enough to freeze most motion.

On the other hand, if there is enough ambient light compared to the shutter duration that that does contribute meaningfully to the exposure, you may get a double image — a sharp image from the flash, plus ghosting. See What is "Dragging the Shutter"? and How does dragging the shutter work? for more on this, as well as When should you use a normal flash vs a second-curtain flash?

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Without seeing an actual example the answer is no. The flash does not reduce any motion blur given the exact same conditions. The exact ones.

But it can give you a diferent ilusion. As the flash gives you a image frozen in time, the aditional motion blur, gives you the ilusion that that motion blur is now a trail.

If you have no defined image, all you see is the motion blur.

But the amount of it is not reduced at all.

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