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

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SUMMARY

The discussion centers on the correct expression for the position function xc(t) in a classical mechanics problem involving a car and a bicycle. The two proposed equations, xc = v0t - c(t - t1)^3 / 6 and xc(t) = v0t1 + v0(t - t1) - c(t - t1)^3 / 6, are shown to be equivalent but neither is the definitive answer. The variable "t" represents any time, and the function xc(t) is identified as a piecewise continuous function, specifically a spline function, which is both continuous and piecewise polynomial in t.

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  • Study the properties of piecewise continuous functions in classical mechanics.
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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!
 
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##.
 
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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