How do I find the position function when i'm given a velocity function?

Question

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

Answer 1

Velocity is the derivative of distance with respect to time. Right? V = dx/dt. So integrate the velocity expression with respect to time to get an expression of the distance travelled.

Answer 2

Do you know how to do integration? If you do, please do not read below. If you do not, then read the following:
v(t)= (6.0m/s^2)t + (3.0m/s),
clearly the first term is the accelaration times time t, and the second term is a constant velocity part.
For the first term, we know that part is zero when t is zero, and it increases linearly with t. Thus for a period of t, the "average" of this first part is just half of it. To time t to get the distance: 0.5*{(6.0m/s^2)t}*t. For the second constant velocity part, you know the distance is just vt. Therefore,
D = 0.5*(6.0m/s^2)t^2 + (3.0m/s)t, is the final result.