Hypothesis: Every object that falls in minecraft has it's own "Acceleration constant" which can be calculated based on tests in freefall. This acceleration constant can then be applied into an equation like d=Vi(t)+(1/2)a(t^2) [the formula for displacement, which can be rearranged to solve for the amount of time something will take to fall] where Vi is initial velocity, a is the acceleration constant, d is displacement, and t is time.
First Test: Falling PlayersTo set up this experiment, I found a long, flat area with which to... well... drop myself onto.
Firstly I set up 3 instances, 10 Blocks high, 20 Blocks high, and 30 blocks high.
I dropped myself 7 times from each height, and recorded the time from the moment I began to fall, until I hit the ground. I then found the average fall time from each height. I proceeded then to use these two values to find the average velocity of the fall from each height. Because initial velocity is 0, I was able to calculate the final velocity of each fall, therefore allowing me to calculate the acceleration experienced during each fall. After finding the acceleration for all 3 instances, I decided to average them together and come up with an average player acceleration for minecraft. The number I came up with is 36.79113231 Blocks/ Second^2.
Player Fall Data (Click to see data)  Spoiler:

My data:
10 block fall:
Trial 1: .633s
Trial 2: .745s
Trial 3: .700s
Trial 4: .700s
Trial 5: .633s
Trial 6: .636s
Trial 7: .760s
Avg: .68671429s
20 block fall:
Trial 1: 1.020s
Trial 2: 1.000s
Trial 3: 1.147s
Trial 4: 1.020s
Trial 5: 1.020s
Trial 6: 1.017s
Trial 7: 1.171s
Avg: 1.056428571s
30 block fall:
Trial 1: 1.412s
Trial 2: 1.284s
Trial 3: 1.352s
Trial 4: 1.275s
Trial 5: 1.408s
Trial 6: 1.418s
Trial 7: 1.418s
Avg: 1.366714286s
Final velocities of each height (calculated by multiplying average velocity by 2, because intitial velocity is 0):
10 block fall: 29.1241937 Blocks/Second
20 block fall: 37.8634122 Blocks/Second
30 block fall: 43.90090928 Blocks/Second
The final velocity is equal to the change in velocity, because initial velocity is 0. This allows us to calculate the acceleration of each fall, (A= Change in Velocity/time):
10 block fall: 42.41093294 Blocks/Second^2
20 block fall: 35.84096667 Blocks/Second^2
30 block fall: 32.12149732 Blocks/Second^2
Average acceleration of the falls: 36.79113231 Blocks/Second^2, in the downward direction.
Second Test: Falling Sand/GravelJust as a given, falling sand and gravel fall at the same rate, their acceleration constant is the same. They do indeed accelerate at a different rate than player and items. To test their rate of acceleration, I built structures 6 blocks, 11 blocks, and 16 blocks high. I then placed the sand block on the uppermost block, allowing it to fall [x1] blocks (5, 10 and 15). I used my trusty stopwatch to take the time it took for 20 trials of each to fall.
The rate of a sandblock accelerating downward is on average about 9.970022187 Blocks/Second^2.
Sand/Gravel Fall Data (Click to see data) Spoiler:

My data:
5 block fall average time: 1.01885 seconds
10 block fall average time: 1.3769 seconds
15 block fall average time: 1.7566 seconds
Final velocities of each height (calculated by multiplying average velocity by 2, because intitial velocity is 0):
5 block fall: 9.814987486 Blocks/second
10 block fall: 14.52538311 Blocks/second
15 block fall: 17.078447 Blocks/second
The final velocity is equal to the change in velocity, because initial velocity is 0. This allows us to calculate the acceleration of each fall, (A= Change in Velocity/time):
5 block fall: 9.636235321 Blocks/second^2
10 block fall: 10.5493372 Blocks/second^2
15 block fall: 9.72445364 Blocks/second^2
Average acceleration of the falls: 9.970022187 Blocks/second^2, in the downward direction.
Third Test: Falling ItemsAll items [the definition of item: anything you can put in the inventory and drop on the floor] fall at the same rate. This can be observed by placing any kinds of items on top of a glass block, over a drop. All of them will fall in the same formation they were on the glass block. To calculate the rate of falling of items I created a 10 block drop with a pressure plate at the bottom, which would light up a red torch at the top [the 10 block drop allowed for instantaneous transmission of the electric current, there didn't seem any need for an offset] and allow me to note the time with a stopwatch. [There was also... y'know... looking down at the drop and hearing the sound of the pressure plate that let me get more accurate measurements]. This result is more tentative than the others, seeing as I only tested it 10 trials in 1 experiment, as the others I tested multiple times. The results so far are that items accelerate downward at a speed of 14.03523741 Blocks/second^2
Item Fall Data (Click to see data) Spoiler:

After 10 trials of items I came up with an average time of 1.193727273 seconds.
10 blocks/1.1927273 seconds = 8.37712839 Blocks/second [this is only an average velocity]
8.37712839 Blocks/second * 2 = 16.75424568 Blocks/second Final Velocity [because intial velocity is 0]
16.75424568 Blocks/second over 1.193727273 seconds = 14.03523741 Blocks/second^2 in the negative direction
Fourth Test: Running SpeedI just thought I'd add this in here... It's not about freefall. The max velocity running speed seems to be 4 Blocks/Second in a straight line.
Running Speed Data (Click to see data) Spoiler:

I ran a 10 block straight line and timed myself, usually getting around 2.5 seconds each time. 10 blocks/2.5 seconds = 4 Blocks/second.
Fifth Test: Max Minecart SpeedThe max minecart velocity seems to be 8.148 Blocks/Second. However it makes more sense to round it off to 8.
Minecart Speed Data (Click to see data) Spoiler:

I created a hugeeeeee minecart ramp, to the top of the map, down around 70+ blocks. This ramp was way more than enough to reach a constant top speed. Then the track flattened out, and on the sides were 2 torches. Time began at these 2 torches, until the end of a 44 block straight stretch. The minecart traversed this stretch in 5.4 seconds almost every time. The standard deviation was around 0.100 in either direction. 5.4 seconds/44 blocks = 8.148 Blocks/Second
Conclusions/TL;DR  Players accelerate at a rate of:
36.79113231 Blocks/ Second^2.Sand/Gravel accelerates at a rate of:
9.970022187 Blocks/Second^2.Items accelerate at a rate of:
14.03523741 Blocks/second^2 Players run [straight] at a max velocity of:
4 Blocks/secondMincarts travel [straight] (With a player in it) at a max velocity of:
8 Blocks/second _______________________________________________
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