Basic Kinematics - shouldn't there be a constant?

[Taulant Sholla]

Homework Statement

Homework Equations

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

The Attempt at a Solution

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.

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?
None of the given initial conditions seem to indicate that a(0)=0.

Thank you!

 

[BvU]

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

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.

 

[Doc Al]

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.

 

[Taulant Sholla]

Ach - yes, thank you. Pretty embarrassing