Calculating Altitude of an Object From Acceleration?

Question

Is is possible to calculate altitude of an object shot upwards, from having acceleration and time throughout the flight (as well as velocity).

Answer 1

You would also need the angle at which the object was fired. I''m assuming that the object cannot provide its own thrust, and air resistance is negligible, in which case, the only forces acting on the object in the air the force of gravity. This means that it has an acceleration (due to gravity) of 9.81 m/s² [down]. Knowing this in conjunction with either velocity or time will allow you to solve for the height of the object by means of specific kinematics equations.

Even if you decided to incorporate air resistance or if other forces interacted with the object you could still determine the height/altitude of the object using acceleration, time and velocity; it's just that with more considerations, the math becomes more complicated.