Help me to clear my doubt about a problem of Classical Mechanics (Car and Bicycle)

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Homework Help Overview

The discussion revolves around a problem in classical mechanics involving the motion of a car and a bicycle. Participants are examining two expressions related to the position of the car over time and questioning their validity in the context of the car's stopping condition.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are comparing two mathematical expressions for the car's position and questioning how these reflect the car's stopping time. There is a focus on the continuity and piecewise nature of the function representing the car's motion.

Discussion Status

Some participants have provided hints regarding the nature of the function, suggesting it is piecewise continuous and possibly a spline function. There is an ongoing exploration of the implications of these characteristics on the problem at hand.

Contextual Notes

There is mention of a bicycle, indicating that there may be additional parts to the problem that have not yet been addressed. The discussion also highlights the importance of understanding the definitions and conditions related to the motion of the car.

Ishfa
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Homework Statement
Is the answer, xc = v0t -c( t - t1 )^3 /6 or xc(t)=v0t1+v0(t−t1)−c(t−t1)^3 /6 ? Which one is correct and why?
Relevant Equations
a = -c (t - t1)
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Ishfa said:
Homework Statement: Is the answer, xc = v0t -c( t - t1 )^3 /6 or xc(t)=v0t1+v0(t−t1)−c(t−t1)^3 /6 ? Which one is correct and why?
Those two expressions are equal!
 
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The expressions may be equal, but neither of them can be considered the answer. Variable "t" in these expressions is "any time t". How do these answers reflect the fact that the car stops at t = t2?
Hint: xc(t) is a piecewise continuous function.
 
Last edited:
kuruman said:
Hint: xc(t) is a piecewise continuous function.
It's actually a continuous function.
 
PS it's actually a Spline function - continuous and piecewise polynomial in ##t##.
 
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PeroK said:
PS it's actually a Spline function - continuous and piecewise polynomial in ##t##.
I defer the appellation details to you. I just wanted to convey the "piecewise" and "continuous" ideas to the OP.
 
What's with the bicycle? Is there a part (b)?
 

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