Train/Car acceleration/speed problem

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SUMMARY

The discussion centers on a physics problem involving a train moving at a constant speed of 24 m/s and a car initially 49 m behind, traveling at 37 m/s and accelerating at 4 m/s². The solution involves using the equation 2aΔx = v² - Vo² to determine the car's final velocity as it passes the train. The calculated speed of the car is approximately 41.96 m/s. The challenge lies in understanding how the train's speed influences the car's speed at the moment of passing.

PREREQUISITES
  • Understanding of kinematic equations, specifically 2aΔx = v² - Vo²
  • Knowledge of acceleration and its effects on velocity
  • Familiarity with relative motion concepts in physics
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the concept of relative velocity in physics
  • Learn more about kinematic equations and their applications
  • Explore problems involving acceleration and constant speed scenarios
  • Investigate graphical representations of motion to visualize speed and acceleration
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This discussion is beneficial for physics students, educators, and anyone interested in understanding motion dynamics, particularly in scenarios involving relative speeds and acceleration.

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Homework Statement


A train is moving parallel and adjacent to a highway with a constant speed of 24 m/s. Initially a car is 49 m behind the train, taveling in the same direction as the train at 37 m/s, and accelerating at 4 m/s/s.

What is the spped of the car just as it passes the train? Answer in units of m/s.



Homework Equations



I used 2aΔx=v^2-Vo^2


The Attempt at a Solution



I was solving for the car to get its final velocity (v^2) when it passes the train:
2aΔx=v^2-Vo^2
2(4m/s/s)(49m)=V^2-(37m/s)^2
392 m^s/s^2=V^2-1369 m^2/s^2
1761 m^2/s^2=V^2
41.96427 m/s=V (for the car)

my problem is that I don't know how to accommodate for the trains speed and how it effects the speed of the car as it passes. i know that the car will have to go faster but I just don't know how to approach the problem
 
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