Position Functions for Two Cars Colliding on a Straight Road

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SUMMARY

The discussion centers on calculating the collision point of two cars, Car A and Car B, approaching each other on a straight road. Car A travels at 16 m/s and decelerates at 2 m/s², while Car B moves at 8 m/s and decelerates at 4 m/s. The initial distance between the cars is 45 meters. The solution involves deriving position functions for both cars over time to determine the exact time and location of the collision.

PREREQUISITES
  • Understanding of kinematic equations for uniformly accelerated motion
  • Knowledge of basic algebra for solving equations
  • Familiarity with concepts of relative motion
  • Ability to graph functions to visualize motion
NEXT STEPS
  • Learn how to derive position functions from velocity and acceleration
  • Study the kinematic equations for one-dimensional motion
  • Explore relative motion concepts in physics
  • Practice solving collision problems using different initial conditions
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Students studying physics, particularly those focusing on kinematics and motion analysis, as well as educators looking for practical examples of collision problems.

Jesper K
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Homework Statement


Two cars approach each other on a straight road. Car A is moving at 16m/s and car B at 8m/s. When they are 45m apart both drivers apply their brakes. Car A slows down at a rate of 2m/s^2 while car B slows down at 4m/s^2. Where and when do the cars collide?

Homework Equations



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The Attempt at a Solution


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I don't really understand this so i would appreacite if someone could help me
 
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Can you write the position as a function of time for each car? (Let the initial position of Car A be x = 0. What would be the initial position of Car B?)
 

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