#kinematics
I’ve been away expending my knowledge on theories, its subtopics and concepts. I’ve barely scratched the surface of kinetics, but hey; big things start will small steps.
You would be forgiven for assuming that heavier objects fall faster than lighter ones—it sounds like common sense, and besides, you know for a fact that a bowling ball drops more quickly than a feather. And this is true, but it has nothing to do with gravity—the only reason this occurs is because the earth’s atmosphere provides resistance. In reality, as Galileo first realized about 400 years ago, gravity works the same on all objects, regardless of their mass. What this means is that if you repeated the feather/bowling ball experiment on the moon (which has no atmosphere), they would hit the ground at the exact same time.
… is a differential equation:
where acceleration a(t), velocity v(t), and displacement s(t) are all vectors and functions of time. This equation is second-order in position because the highest derivative is the second time derivative of position. Combined with the right boundary conditions, s(t) (also called the trajectory: path through space and time) can be determined.
This differential equation can be solved one component, or dimension, at a time. Let us focus on one of these, and call it the x component. The equations for y and z can be found exactly the same way.
Constant acceleration
If the graph of a(t) signifying acceleration in the x direction is constant
then the graph of v(t), the velocity in the x direction, is a straight line with slope a0
and the graph of x(t), the position along the x axis, is a parabola
It is also possible for the acceleration, or either of the initial velocity or initial position, to be negative. Thus the displacement/projectile motion formula is derived.