How long would it take for a person to sprint from the 0m line to the 100m line if they are traveling forward at 6m/s?

This section assumes you have enough background in calculus to be familiar with integration. In Instantaneous Velocity and Speed and Average and Instantaneous Acceleration we introduced the kinematic functions of velocity and acceleration using the derivative. By taking the derivative of the position function we found the velocity function, and likewise by taking the derivative of the velocity function we found the acceleration function. Using integral calculus, we can work backward and calculate the velocity function from the acceleration function, and the position function from the velocity function.

Explanation:

Derive the kinematic equations for constant acceleration using integral calculus.Use the integral formulation of the kinematic equations in analyzing motion.Find the functional form of velocity versus time given the acceleration function.Find the functional form of position versus time given the velocity function.