A really tough physics math problem that I am in major need of help with

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SUMMARY

Tara is driving at 30 m/s and encounters Sean's van, which is 155 meters ahead and moving at 5 m/s. Due to wet road conditions, Tara can only decelerate at -2.00 m/s². To determine if a collision occurs, one must establish the position functions for both vehicles over time and solve for potential intersection points. The analysis confirms whether a collision happens and calculates the distance and time of occurrence if it does.

PREREQUISITES
  • Understanding of kinematic equations for motion
  • Familiarity with concepts of acceleration and deceleration
  • Ability to solve quadratic equations
  • Knowledge of relative motion in physics
NEXT STEPS
  • Study kinematic equations in detail, focusing on position as a function of time
  • Learn how to derive and solve equations for constant acceleration
  • Research relative motion scenarios in physics
  • Practice problems involving collisions and distance calculations
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Students studying physics, particularly those tackling kinematics and motion problems, as well as educators looking for examples of collision analysis.

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Homework Statement



Tara, driving at 30 m/s, enters a one-lane tunnel. She then observes Sean's slow moving van 155m ahead traveling at 5 m.s. Tara applies her brakes but can accelerate at only -2.00m/s/s because the road is wet. will there be a collision? if so, determine how far in the tunnel it occurs and at when it occurs. If not, determine the final distance between Tara and Sean.

Homework Equations





The Attempt at a Solution


i don't know where to start!
 
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Start by writing expressions for the position of each as a function of time. (One motion is just constant speed, the other is accelerated.) Measure the position of each from the tunnel entrance.

Once you have those expressions, you can solve for when and where they collide--if they do.
 
okay thanks! ill try that!
 

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