Acceleration in 1 dimension (Conceptual)

AI Thread Summary
Two cars, C and D, are traveling in the same direction, with car D initially ahead and accelerating while car C is slowing down. Despite car C decelerating, it can still gain on car D if its speed is initially greater than that of car D. The key to understanding this scenario lies in the relative velocities; if car C's speed is higher than car D's at the start of the interval, it can close the gap even while slowing down. The discussion highlights the importance of initial velocities and acceleration rates in determining the distance between the two cars. Ultimately, the resolution of the confusion reveals that car C must have had a greater initial velocity than car D for the gap to decrease.
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Homework Statement



Two cars C and D travel in the same direction on a long, straight section of a highway. During a particular time interval \Deltat0, car D is ahead of car C and speeding up while car C is slowing down.

During the interval \Deltat0, it is observed that C gains on car D (i.e.e the distance between the cars decreases. Explain how this is possible.

The Attempt at a Solution


I'm not sure, but what I thought was that if car C gains distance and slowing down, the change in its velocity (acceleration) over the very beginning of this time interval is lower than cars D acceleration in that beginning of the time interval. That way car C maintains the relatively same velocity for that small time period and can "gain". But then if car D is accelerating at a greater rate, then how could car C gain on car D? Can we assume the initial and final velocities differ for each car? I'm very confused.
 
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The answer is very simple. If car D is ahead and speeding up, and car C is slowing down but the gap decreases then how must the velocities of the two compare? That is, which has the greater velocity?
 
Cart C. Wow that was very simple... thanks
 
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