Final answer:
To find the velocity function and position function given the acceleration function, initial velocity, and initial displacement, you can integrate the acceleration function to find the velocity function and then integrate the velocity function to find the position function.
Step-by-step explanation:
To find the velocity function and position function given the acceleration function, initial velocity, and initial displacement, we can use calculus and the kinematic equations. The velocity function can be obtained by integrating the acceleration function with respect to time, taking into account the initial velocity. The position function can then be found by integrating the velocity function with respect to time, considering the initial displacement.
Step-by-step:
- Integrate the acceleration function with respect to time, considering the initial velocity, to find the velocity function. This is done by finding the antiderivative of the acceleration function and adding the constant of integration.
- Integrate the velocity function with respect to time, taking into account the initial displacement, to find the position function. Again, find the antiderivative of the velocity function and include the constant of integration.