On the meaning of the second derivative When we want to find the velocity of an object we use the derivative to find this. However, I just learned that when you find the acceleration of the object you find the second derivative. 
I'm confused on what is being defined as the parameters of acceleration. I always thought acceleration of an object is it's velocity (d/t). 
Furthermore, in the second derivative are we using the x value or the y value of interest. In the first derivative we were only concerned with the x value. Does this still hold true with the second derivative?
I would post pictures but apparently I'm still lacking 4 points. 

The position function is typically denoted $r=x(t)$. Velocity is the derivative of the position function with respect to time: $v(t)=\dfrac{dx(t)}{dt}$. Acceleration is the derivative of the velocity function with respect to time: $a(t)=\dfrac{dv(t)}{dt}$. This is equivalent to the second derivative of the position function with respect to time: $$\dfrac{d}{dt}\dfrac{d}{dt}x(t)=\dfrac{d}{dt}\dfrac{dx(t)}{dt}=\dfrac{d}{dt}v(t)=\dfrac{dv(t)}{dt}=a(t).$$
The derivative is taken because it gives the change of a function with respect to its input variable.
