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 $t$ is your only variable.

Therefore, consider the following,

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

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

Once you figure that out repeat for $v(t)$ and $d(t)$.

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,

$${a(t)} = {\int_{}^{}}{K}{dt}$$

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