How Do You Derive the Final Equation for Displacement and Time?

[Anita08]

In order to get this final equation
of Displacement and time: $$v(t) = v_0 + \frac{1}{2} a t^2$$


How would I come about actually making this equation?

Would it be a combination of the simple acceleration equation and Delta x equation ... with so algebra. BOOM answer?


Thanks for your help!

--- Anita

 

[diazona]

um... actually that isn't a correct equation. Were you thinking of one of these?
$$\begin{align*}<br /> x(t) &= x_0 + v_0 t + \frac{1}{2}a t^2 \\<br /> v(t) &= v_0 + a t<br /> \end{align*}$$

 

[Anita08]

Oh, crap yes! The first one :)

 

[drizzle]

http://www.coolschool.ca/lor/PH11/unit2/U02L02/kinematic5.gif"
make sure you understand it

 

[Anita08]

WOW, that's how you do that! UH, I hate not having math hard core in my life and then BAM all of a sudden need to use it.

Thanks a million :) !

 

[berkeman]

Oh, crap yes! The first one :)

Are you comfortable with doing integrals in calculus? You use fairly simple integrations to go from a(t) --> v(t) --> x(t), assuming constant acceleration (which is true in this case of gravity being the acceration).

 

[Anita08]

I used to about two years ago :(

I'm lost at times but definitely getting there!

 

[drizzle]

any time