Acceleration in 1 dimension (Conceptual)

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SUMMARY

In the discussion titled "Acceleration in 1 dimension," participants analyze a scenario where car C, despite slowing down, gains on car D, which is accelerating. The key conclusion is that car C must have a greater initial velocity than car D for the distance between them to decrease, even as car D accelerates. This situation highlights the importance of understanding relative velocities and acceleration in one-dimensional motion. The confusion arises from the interplay between acceleration rates and initial velocities.

PREREQUISITES
  • Understanding of basic kinematics, including velocity and acceleration.
  • Familiarity with the concepts of relative motion and how they apply to moving objects.
  • Knowledge of the equations of motion for uniformly accelerated objects.
  • Ability to analyze motion graphs and interpret changes in velocity over time.
NEXT STEPS
  • Study the equations of motion for uniformly accelerated motion in physics.
  • Learn about relative velocity and its applications in different frames of reference.
  • Explore graphical representations of motion, including velocity-time and acceleration-time graphs.
  • Investigate real-world applications of kinematic principles in automotive engineering.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of motion and acceleration in one dimension.

skwz
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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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