Motion with Constant Acceleration help

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SUMMARY

The discussion focuses on solving a motion problem involving two cars with constant acceleration. Car 1, starting at mile marker 0, travels east at 18.0 m/s with an acceleration of 0.40 m/s². Car 2, initially 0.90 km east of mile marker 0, travels west at 30.0 m/s while decelerating at 0.80 m/s². The key to finding the point where the two cars meet is setting their position equations equal to each other: x1 = x2.

PREREQUISITES
  • Understanding of kinematic equations for motion with constant acceleration
  • Familiarity with algebraic manipulation of equations
  • Knowledge of vector direction in motion problems
  • Basic concepts of acceleration and deceleration
NEXT STEPS
  • Study kinematic equations in detail, focusing on position, velocity, and acceleration relationships
  • Learn how to solve quadratic equations, as they often arise in motion problems
  • Explore graphical representations of motion to visualize the problem better
  • Practice similar problems involving multiple objects with different accelerations
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone seeking to understand motion with constant acceleration, particularly in the context of solving problems involving multiple moving objects.

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Homework Statement


Two cars drive on a straight highway. At time t = 0, car 1 passes mile marker 0 traveling due east with a speed of 18.0 m/s. At the same time, car 2 is 0.90 km east of mile marker 0 traveling at 30.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 0.40 m/s^2, and car 2 is slowing down with an acceleration of magnitude 0.80 m/s^2.



Homework Equations



I have used that data to create an X vs T equation
x1=(18.0 m/s)t+(0.2)t^2;\;x2=900 m -(30.0 m/s)t+(0.4)t^2



The Attempt at a Solution



I cannot show an attempt because i have searched in the book how to find where they meet and am unsuccessful. Can anyone tell me how to figure this out starting from the beginning? Thank You!
 
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You seem to have been careful with the signs, and your equations look correct.

If you set x1 = x2, you will find the time instant at which they meet.
 

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