answer ⇒ When they have same speed or same velocity.
Explanation ⇒ The Cyclist Appears to be Stationary with respect to the another moving cyclist only when the speed of both the cyclist is same.
When the Speed or you can say that the velocity of the Cyclist is same, then both appears to be at rest with respect to one another.
One term should be noted here that ''with respect to'' which means, only when they are seen with respect to each other. If we will compare there state of Rest or Motion with some ground observers than they will not be stationary.
But, they will be stationary with respect to the each other.
Hope it helps.
question: When does the cyclist appear to be stationary with respect to another moving cyclist
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.
Hope it helps
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if your are asking why then
it happened because of frame of reference.
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