Your video does not actually show what you are apparently wanting. The cloud actually moves positions and does not leave an aftertrail.
As mentioned this can be done using a video editor to place the various images together.
You also mentioned the example of traffic stills which inclide the lights of cars and making it look as if you are getting car trails.
You could from one image:
1. Duplicate it say 4 times
2. Turn off visibility of the top 4 layers
3. Apply motion blur - Adjust > Blur > Motion Blur and select the directio of blur and increase the strength to get the amount of blur you want.
4. Make layer 2 active (counting up from bottom) , reduce its opacity to about 40
5. Use move tool to move the layer 2 image in the direction of the blur til it aligns with the last part of the blur from layer 1
6. Increase opacity to max. Apply motion blur.
7. Repeat this procedure with each of the other layers.
8, Change the blend mode of each of the layers except the first one to Screen.
This
will give an extended blur .
Roughly done.
Of course the easiest way is to set your camera up on a tripod at night and use a long exposure.
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