Answer:
To represent the motion of an object (ignoring rotations for now), we need three functions x(t), y(t), and z(t), which describe the spatial coordinates of the object for each
possible time. Since there are an infinite number of possible times (between any starting and ending time), giving the coordinates at all possible times is actually an infinite
amount of information!
Part of the magic of physics is that we can predict all of this information knowing
only the initial position ⃗r(t = 0) = (x(t = 0), y(t = 0), z(t = 0)) and velocity ⃗v(t = 0) =
(vx(t = 0), vy(t = 0), vz(t = 0)) of an object, plus the information about the object’s
environment (specifically, what forces are acting on it). The key tool is Newton’s
Second Law, which we write as:1
⃗a =
1
m
F⃗NET . (1)
This says that we can predict the acceleration of an object by knowing the forces on the
object. We are assuming that the object’s environment is understood well enough that
we can predict the forces on the object from the object’s position and velocity
:⊃