How Long Does It Take for an Accelerating Car to Overtake Another?

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SUMMARY

The discussion centers on calculating the time it takes for Car B, which has a constant positive acceleration, to overtake Car A, which is 25 meters ahead and moving at a constant velocity. The calculation involves understanding the principles of Galilean relativity, where the problem can be analyzed from Car A's reference frame. The conclusion is that the time required for Car B to cover the 25 meters is not simply the time taken from a standing start, due to the acceleration factor. This highlights the importance of applying the correct physics principles to solve motion problems.

PREREQUISITES
  • Understanding of basic kinematics, including velocity and acceleration
  • Familiarity with Galilean relativity concepts
  • Knowledge of equations of motion for uniformly accelerated objects
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the equations of motion for uniformly accelerated objects
  • Learn about Galilean relativity and its applications in physics
  • Explore examples of relative motion problems in physics
  • Practice solving kinematic problems involving acceleration and constant velocity
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding motion dynamics, particularly in scenarios involving acceleration and relative motion.

APett
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Say we have two cars, Car A and Car B. Car A is 25 meters ahead and has a constant velocity. Car B has the exact same velocity at this moment, but also has a constant positive acceleration. If I want to calculate how long it takes for Car B to overtake Car A, wouldn't it be the same as calculating how long it takes car B to go 25 meters from standing still? I'm fairly sure it is, but I'm new to physics and afraid there's something I'm missing.
 
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Sorry, I just realized it's probably the wrong subforum. Can someone move it?
 
You are correct. You are using special relativity (or Galilean relativity). You can translate the problem to the car A reference frame.
 

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