Putting it all together (calc and physics)

[LT72884]

Ello all. Ok so I am excited. i am taking my first ever physics class, calc based. SO I am trying to relate things from calc to physics because i am some what confused.

In calc we learned that if you have P(t)= t^2 + 5t +6

this is a position function. You plug in time (t) and it will give heght P(t) back. I also know if oyu take the deriv of said function and then plug in time (t), you get velocity. Take second deriv and plug in time (t) if applicable and you get acceleration in m/s^2

thats all fine and cool. but now I am given some wacked out equations

for example. i was sked to find acceleration of an ice skater after she hits a rough patch of ice. I got the answer right because it is just plug and chug, however, i don't like plug and chug. i want to know what's going on

the equation i used was

Vfx^2=Vix^2+2a(delta x)

my question is this. is the above equation a second deriv of some funky P(t) function? How is the above equation related to derivs? How did they come up with said equation. my book does not say, it just gives the equation.

im trying to relate the equation to calculs so i can understnad this better.

i do know that with position vs time graphs, where are looking at measurements of velocity, and with velocity vs time graphs, we are looking at measurments of acceleration.

thanks

 

[milesyoung]

It's a basic kinematic relationship in motion with constant acceleration:
http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot5

You integrate both sides of $\frac{\mathrm{d^2}x}{\mathrm{d}t^2} = a$ a couple of times and go through a bit of algebra.