Lovers Reunited: Calculating Time Apart

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SUMMARY

The discussion centers on calculating the time it takes for a couple to reunite after being 30.0 meters apart, with the husband accelerating from rest at 0.7 m/s² and the wife moving at a constant speed of 3.4 m/s. The husband’s distance traveled can be expressed using the equation of motion, while the wife’s distance is linear. By setting the equations for their distances equal, the time until they meet can be determined through algebraic manipulation.

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  • Understanding of kinematic equations, particularly for uniformly accelerated motion.
  • Familiarity with basic algebra for solving equations.
  • Knowledge of relative motion concepts.
  • Ability to interpret and manipulate distance-time relationships.
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  • Study kinematic equations for uniformly accelerated motion.
  • Learn how to derive distance equations from velocity and acceleration.
  • Explore relative motion problems in physics.
  • Practice solving real-world problems involving acceleration and constant speed.
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This discussion is beneficial for physics students, educators, and anyone interested in understanding motion dynamics, particularly in scenarios involving acceleration and relative speed.

Shane_K
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I have a question which reads as follows:
After a long time apart, a young couple in love are running towards each other in the hallways of an airport. They are 30.0m apart. The husband is accelerating from rest at a rate of 0.7m/s2 (2 is squared), and the wife was moving at 3.4m/s and maintains her speed. How much time passes before they are finally together?

I just need help gathering the info from the question.
What I have so far:
Husband
-v1=0m/s
-acceleration=0.7m/s2 (2 is squared)
-distance=30.0m
-time=?

Wife
-v1=3.4m/s
-distance=30.0m
-t=?

Thanks in advance:)
 
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One may infer from the problem that the husband starts accelerating when his wife is 30 m from him. During the same period of time, each is traveling to some common point.

Let x be the distance traveled by the wife, and then knowing the velocity that the wife travels, 3.4 m/s, the distance as a function of time is simply x = 3.4 t (t in seconds).

In the same time, when they meet, the husband must have traveled 30-x.
 

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