Newton’s Second Law
Newton’s second law states that as mass increases the acceleration decreases and as mass decreases the acceleration increases. This can also be written by saying that the mass is inversely proportional to the acceleration (a~1/m). The force on an object is directly proportional to the acceleration so as the force increases the acceleration increases and if the force decreases then the acceleration decreases (a~F). These two expressions can be combined to relay Newton’s second law (a=F*1/m or a=F/m).
Mass and weight are two different things, the mass is how much stuff is in the object and the weight is the force of gravity on the object. If the mass is know we can discover the weight of the object through the formula weight=mass*Force due to gravity (w=mg).
In a free fall there is no air resistance and the objects weight is not taken into account. These objects are all falling at the same rate (force of gravity 10m/s^2).
The ball is dropped over the edge of a cliff and it takes it about 10 seconds to hit the ground at the bottom. In this the ball is falling at a constant acceleration of 10m/s^2. At 0 seconds the ball is at rest and has an a (acceleration) of 0m/s^2 and a v (velocity) of 0m/s. After you drop it at the first second the a = 10m/s^2 and the v=10m/s. After the 3rd second the a =10m/s^2 and the v =20m/s. this continues until the ball hit the ground. The formula to find the distance it has fallen is distance=1/2gravity*time^2 (d=1/2gt^2). To find the speed it was travelling the formula is velocity=gravity*time (v=gt).
With a rock you throw it up into the air and it travels a distance and falls back into your hand. What is happening here is that the initial velocity that it was given by the throw is weakened over time as gravity acts on it and falls back down to the point from which it was thrown. The distance it travels upward depends on the initial velocity. The force of gravity is placing a downward acceleration of 10m/s^2 and every second that the rock is in the air the velocity decreases by 10m/s until it is moving at 0m/s. Here it is at the top of its path and begins to fall downwards. The formulas to find the distance and the velocity are the same as falling down d=1/2gt^2 and v=gt. The only difference is that the distance formula can only measure a downward distance. If you desire to find an upward distance you must find the distance that it fell the remaining amount of time and subtract that from the total distance it fell.
Projectile motion down
Here the rock is thrown straight off the cliff with a velocity of 10m/s. The explanation above of Falling Down applies here as well as the velocity of 10m/s. The velocity is constant and so the rock falls at the same rate and is moving at a velocity of 10m/s making it land somewhere out front of the cliff not directly below it. The vertical velocity and distance is explained in the Falling Down and the horizontal velocity is found through the formula of velocity=distance/time (v=d/t) and the distance that it moves from the origin is found through the formula distance=velocity*time (d=vt). So instead of moving forward and the down like a stair case the rock moves in a diagonal arc.
Projectile motion up
Here the rock is thrown up and forward at the velocity of 10m/s. The same explanation of Throwing up is used for the vertical velocity and distance and the formula v=d/t and d=vt are used to find the horizontal velocity and distance. The path of the rock is a diagonal arc to the location of it hitting the ground.
Here air resistance applies and air resistance it the force of air pushing against you or an object. The higher the velocity or surface area the higher the air resistance. When you jump out of a plane your downward force is the weight of the object and you will continue to accelerate until the air resistance is equal to your downward force. Once this happens this is called terminal velocity and the acceleration stops and the velocity becomes constant. When you open your parachute the surface area dramatically increases and the air resistance does as well. Over time the air resistance will decrease and the velocity will as well until it equals the downward force. This is the second terminal velocity is at a much slower velocity because the surface area is larger.