So i have to do a lab in my physics class. i collected data points on the distance traveled and time it took for a ball in free fall (as free fall as you can get) and i need to figure out the speed of the object. the tricky part is, i'm dealing with intervals of 1/60 of a second and the distance in measured in millimeters.

i'll give you an example (using random numbers):

distance = 300 mm, time = 15/60 s

now i know how to calculate speed - divide the distance traveled from the first point to the point i'm using here (the 15th point) by the time it took to get there. the problem is, the speed needs to be in meters per second, not millimeters per one sixtieth of a second.

the way i have the equation set up is like this;

300 mm / 15/60 s [1 x 10^-3 m/1 mm] [4 15/60 s/1 s]

what i did was i took the original unit of speed (300 millimeters per 15/60th of a second) and i converted the millimeters to meters and the 15/60th of a second to seconds.

the answer i get is 1.2 m/s.

however, i could get another answer by taking the unit 300 and subtracting it from the distance of the interval below it (in this case, we'll say its 250), and then doing it with 1/60th of a second rather than 15/60th of a second.

so like this:

300 - 250 = 50

50 mm / 1/60 s [1 x 10^-3 m/1 mm] [60 1/60 s/1 s]

same equation, but with new values.

the answer i get now is 3 m/s.

now the real reason why i ask this is because i did this to all the points, and now i have to calculate the acceleration for them. i know the acceleration due to gravity is 9.81 m/s^2 (we use 9.8 m/s^2 here), and i've done the lab both ways. i get a different number than 9.8 (we can be a little off), but i seem to get a closer number to that by doing the second formula rather than the first formula.

my question is, how would i calculate the speed with these data points, while still converting it to meters per second?

(quick reminder because i think it may be necessary: the first one uses the distance away from the starting point where time is equal to zero seconds, while the second one is a subtraction of one interval and the interval below it. i very much want to say it's the first equation, but like i said, when calculating the acceleration, i get a closer number with the second equation).

(edit: i don't know why it says i'm at a middle school level. i'm doing high school physics. i can't change it though, sorry about that)