Newton's 2nd Law: Displacement & Trajectory of Motion

[hisham.i]

If we make a diff. equation from Newtons's 2nd law, and solve it, we will get x(t), where x(t) is the displacement as a function of time.
what do the shape of the graph x(t) means?
Does it give the trajectory of the motion?

 

[elibj123]

No, in one dimesnion the trajectory will be a line repeated many times (depends on the motion).

If you go in higher dimension, f.e. 2. You will obtain two functions x(t), y(t). Both graphs again don't give you the trajectory. But if you look at (x(t),y(t)) as simply a parametric description of a curve on the xy plane, then this curve is the trajectory.

 

[HallsofIvy]

If your "x(t)" is a three dimensional vector, say, \vec{x}(t)= <x(t), y(t), z(t)>, then, yes, x(t) gives the trajectory of of the object.

 

[matematikawan]

A trajectory is the path trace out by the particle. In one dimension the path will be a line segment. A graph x against t is a representation of the position of the particle.