Question

when does the cyclist appear to be stationary with respect to another moving cyclist

Answer 1

When both of them are cycling at the same velocity.

Answer 2

hey friend:
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question: When does the cyclist appear to be stationary with respect to another moving cyclist

solution: 

the frame of reference are very important in such cases

In the moving cyclist frame of reference the another cyclist will appear to be 
stationary when they both have same velocity.

From ground Frame of reference he will appear stationary when the velocity is 0 of the cyclist.

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