Final answer:
To find the velocity function and position function when given the acceleration function, integrate the acceleration function twice.
Step-by-step explanation:
To find the velocity function and position function when given the acceleration function, you need to integrate the acceleration function twice.
- First, integrate the acceleration function with respect to time to find the velocity function.
- Next, integrate the velocity function with respect to time to find the position function.
Here's an example: If the acceleration function is a(t) = 3t^2, you would integrate it to find the velocity function v(t) = t^3 + C, where C is the constant of integration. Then, you would integrate the velocity function to find the position function p(t) = (1/4)t^4 + C2t + C3, where C2 and C3 are constants of integration.