Derivative

[shelarson]

What physical quantity does a function represent if its first derivative represents velocity and its second derivative represents acceleration?

This question above is part of a evaluation of an essay I had to write for a Calculus class. I can not pass this task with out answering the above question.

"Instantaneous velocity is found by knowing how much x changes. The formula for instantaneous velocity is ?vt=lim??(?t?0)??(f(t+?t)-f(t))/?t?. Velocity is the speed and direction of an object. The instantaneous velocity formula is the limit definition for the derivative. Velocity is the first and acceleration is the second derivative. Acceleration is the rate change of an object."

The above paragraph is a part of the essay. I can not get my mind around what they are asking. The formula did not transfer very well. Please help me understand what they are asking.

Shelly

 

[BigGlenntheHeavy]

\(\displaystyle s(t) \ = \ Position \ function\)

\(\displaystyle v(t) \ = \ s'(t) \ = \ Velocity \ function\)

\(\displaystyle a(t) \ = \ v'(t) \ = \ s"(t) \ = \ Acceleration \ function\)