An object has a constant acceleration of 30 ft/sec2, an initial velocity of -10 ft/sec, and an initial position of 4 ft. find the position function, s(t), describing the motion of the object.

Let be the acceleration, velocity, and position functions, respectively. Then




Since the acceleration is a constant 30 ft/s^2, you have





You're told that the initial velocity is , so you get



Now . Integrating once more, you find




and since , you get



which means the exact position function is