How to find the position function given the acceleration function

The video tutorial covers solving a particle motion problem by finding the position function. It begins with an overview of the problem, emphasizing the relationship between acceleration, velocity, and position as derivatives of each other. The instructor demonstrates how to integrate the acceleration function to find the velocity function, using given points to solve for constants. Finally, the velocity function is integrated to determine the position function, with a focus on understanding the mathematical process.

What is the final position function derived from the velocity function?

How do you determine the value of C in the position function using the initial conditions?