## Calculus: Early Transcendentals 8th Edition

The definition is $$f''(t)=\lim_{h\to0}\frac{f'(t+h)-f'(t)}{h}.$$ If $f(t)$ is the position function then $f''(t)$ is interpreted as the acceleration.
The second derivative of the function $f$ is the derivative of the derivative of the function $f$. This means that if the derivative is $f'(t)$ then the second derivative is $$f''(t)=\lim_{h\to0}\frac{f'(t+h)-f'(t)}{h}.$$ If $f(t)$ is the position function, then $f'(t)$ is instantaneous velocity and thus $f''(t)$ represents the instantaneous change of the velocity i.e. the acceleration.