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

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The discussion centers on two expressions for the position of a car in classical mechanics, questioning their correctness and relationship. Both expressions are shown to be equal but neither is deemed the final answer due to the variable "t" representing any time. The importance of understanding that the car stops at a specific time, t = t2, is emphasized, highlighting the need for a piecewise continuous function. The conversation also notes that the function is a spline, indicating it is both continuous and piecewise polynomial. The mention of a bicycle suggests there may be additional parts to the problem not yet addressed.
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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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