How Does Relative Motion Affect Perception of Process Speed?

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I'm having trouble understanding the question below. Conceptually I don't see how there would be a difference in speed? Maybe someone can help me shine some light on it...it'd be appreciated!

If you are observing a process moving with respect to you, would you see the rate at which this process proceeds as speeded up or slowed down compared to the same process not moving with respect to you?
 
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time dilation

Per special relativity, a moving clock (or any other temporal process) is measured to run slowly compared to your own clocks (which are at rest with respect to you). The only way to understand how this comes about is to study a bit of relativity.
 
It is a poorly phrased question.
Assume for example you have a process that cycles to produce what you see a green light. The exact same process coming toward you would still produce green light but you would see it a blue light as though the process was running faster. But once this process passed you and was going away it would look red as if it were running slow.

This is a Doppler Effect and is what you would “see” from direct observation. You would need to adjust for that effect to interpret what must be going on in the process even from your perspective (reference frame). When you do you will see that it comes out as running at the same rate coming and going, but slower from your perspective (or reference frame) that it would be as observed by those traveling with the process, (they see the same green as your local process).

As Doc Al said, you need to spend some time working on special relativity for a while to make that part clear.