Basic Kinematics - shouldn't there be a constant?

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Homework Help Overview

The discussion revolves around basic kinematics, specifically the role of constants in the equations for acceleration, velocity, and position. Participants are examining the implications of initial conditions on these equations.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions whether the acceleration function should include a constant, given the initial conditions. Other participants discuss the implications of differentiating and integrating functions in the context of kinematics.

Discussion Status

Participants are actively engaging with the original poster's question, providing insights into the treatment of constants in kinematic equations. There is a recognition of the importance of initial conditions and the differentiation process, though no consensus has been reached.

Contextual Notes

There is an emphasis on the potential confusion arising from using the same symbols for different quantities, as well as the specific initial conditions provided in the problem.

Taulant Sholla
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Homework Statement


probstat.png


Homework Equations


a=dv/dt, v=dx/dt, x=integ(vdt)

The Attempt at a Solution


probsol.png

We were given the above problem and solution. Everything seems very straightforward. My question is this: should the function for acceleration also include a constant, e.g.
alpha.PNG
[/B]
?
None of the given initial conditions seem to indicate that a(0)=0.

Thank you!
 

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Taulant Sholla said:
None of the given initial conditions seem to indicate that a(0)=0.
On the contrary: it is easy to see that ##a(0) = {d\over dt} (\alpha - \beta t^2) \Bigr |_{t=0} = 0##

It is not wise to use the same symbol ##\alpha## for two different things :rolleyes:

A constant only appears if you are given e.g. a velocity and need to calculate the position.
If you have the position as a function of time, the velocity is unambiguous: no constant.

Mutatis mutandis for acceleration and velocity.
 
Last edited:
When you find the acceleration you take the derivative of the velocity function. Only when you integrate a function do you have to add a constant.
 
Ach - yes, thank you. Pretty embarrassing :oops:
 

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