Why the distance increases is because the car switches lanes?

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When a car switches to the left lane to pass another vehicle while maintaining speed, the distance between the two cars increases. This occurs because the passing car travels a longer path compared to the car that continues straight. The time taken to switch lanes contributes to this increased distance. The concept relies on the principle that both cars are moving at constant speeds but along different trajectories. Thus, the distance increases due to the lane change and the differing paths taken.
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Homework Statement


you're driving behind a car and wish to pass, so you turn to the left and pull into the passing lane without changing speed. why does the distance increase between you and the other car you are following?


Homework Equations





The Attempt at a Solution



so in other words the reason why the distance increases is because the car switches lanes to the left and the speed remains constant...so that makes the cars distances greater because of the time taken up by the switching lanes. that was my thought process and i just wanted to know if i was right...?
 
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Sure. You've traveled farther than the car that went straight.
 
thanks easy enough :)
 
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