If I'm given v(t)=(6.0m/s^2)t + (3.0m/s), how do I find the position function?

Question

How do I integrate it?

Answer 1

The rule for integrating terms of a polynomial are easy. Increase the power of the variable by one and divide by that power. For example the integral of x^3 is (x^4)/4. What you have here is an indefinite integral, so you also have to add a constant. The reason for that is, in this example, you have no way of figuring out from the given information what what the initial position was, s(zero).

ds/dt = v(t) = 6t + 3.0
Integrating we get:
s = (6t^2)/2 + 2t + C