## University Calculus: Early Transcendentals (3rd Edition)

For any body moving between two points x and $x_{0}$, the average velocity is given as: $v=\frac{x(t_{1})-x(t_{0})}{t_{1}-t_{0}}$ When the limit is applied at a particular point, it becomes the instantaneous velocity of the body: $v(t_{0})=\lim\limits_{t \to t_{0}}\frac{x(t_{1})-x(t_{0})}{t_{1}-t_{0}}$ Similarly, the acceleration is given as the rate of change of the velocity: $a(t_{0})=\lim\limits_{t \to t_{0}}\frac{v(t_{1})-v(t_{0})}{t_{1}-t_{0}}$