Lab observation correct? As distance decreases, velocity increases, stderr decreases The experiment goes like this: 

Allow a moving cart to move from the top of an incline plane ($x_0$) downwards. The time taken will be recorded by the picket fence (those things you see wired up). Distance ($D$) is reduced by 10cm each time. And a set of recordings are recored as follows: 

Does the recording seem logical? 


*

*As $D$ decreases, $v$ increases? Why, I thought $v$ should reduce as there will be less effect from gravity? 

*As $D$ decreases the standard error decreases. It kind of makes sense as the time interval will be smaller and thus less chance of error. However, I would think if the $D$ is too small, the cart may not have stabalized or something? But that doesn't sound scientific. 

*Is my calculation of standard error right? Or should it be standard deviation here? When do I use which? 

 A: It seems that the cart is always released at the top. It is the first picket fence which is moved. Thus smaller $D$ means you confine the measuring too the high speed regions of the track.
At the last measuring you effectively measure the final velocity of the cart at the bottom.
It's a nice lab, I remember a question about air track --- where the viscous friction take place?
Standard error is the standard deviation of the error. Just standard deviation of the results tells you how do the results scattered. Standard error tells how accurate is the average of the results. You see, the more experiments you do, the more accurate is the average, right?
To answer is your calculation right, you should tell standard error of what quantity are you interested in? In any case, there are too much digits in your STDERR, you should leave in general only 1 significant digit, or maybe 2 for if the first digit is 1.
Basically I suggest you reading your lab book, the beginning. It should tell what are the different quantities, how do you calculate them etc. It is really useful, you read it once for an hour and you are prepared for all the consequent labs, statistics courses, statistics modeling and so on.
