Strange physics question involving no constants and all variables.

[TexasCow]

Homework Statement

"K" is the time derivative of acceleration. Assume initial conditions of Ao, Vo, and Do.("o"=initial).

Find:
a(t):
v(t):
d(t):

Show that:
af^2=ao^2+2J(Vf-Vo)

Homework Equations

I'm honestly lost on this one..I don't know where to start. I could probably do it with numbers but clueless with variables!

The Attempt at a Solution

 

[PFStudent]

Hey,

Remember that what is common between the: displacement, velocity, and acceleration functions; are that they're all functions of time, indicating that [itex]t[/itex] is your only variable.

Therefore, consider the following,

[tex]
{\frac{d}{dt}}{\left[a(t)\right]} = K
[/tex]

So, if the derivative with respect to [itex]t[/itex] was taken to get K, how do you get back [itex]a(t)[/itex]?

Once you figure that out repeat for [itex]v(t)[/itex] and [itex]d(t)[/itex].

Thanks,

-PFStudent

 

[stewartcs]

Hint: Use the Fundamental Theorem of Calculus.

 

[TexasCow]

Integral maybe?

 

[PFStudent]

Integral maybe?

Hey,

Yes. To get you started here is how it looks,

[tex]
{a(t)} = {\int_{}^{}}{K}{dt}
[/tex]

Thanks,

-PFStudent

 

[TexasCow]

Well we haven't gotten there in calc yet but I'm sure I can find out how to do that online somewhere.

 

[stewartcs]

Hint 1: K is the same as K^1
Hint 2: a(t) = K^2/2 + C