Measuring velocity and acceleration: Timer Tape Lab

Watch me do the lab here! This is a video I recorded:http://youtu.be/fQzmv0XRock

Introduction:

The displacement per unit time of a cart will indicated by the placement of ticks on timer tape. Average velocity is equal to the displacement per interval of time, which can be written as v = (x₂ - x₁)/(t₂ - t₁). The instantaneous velocity, at a specific time, is equal to the slope of the displacement vs. time graph, at that specific point in time. The average acceleration is equal to the change in velocity per interval of time, which can be written as: a = (v₂ - v₁)/(t₂- t₁). The instantaneous acceleration at a certain time is equal to the slope of the velocity vs. time graph, at the point on the graph corresponding to that specific time. From the data on the timer tape, you will be able to successively construct graphs to analyze the motion of the cart, plotting first displacement vs. time, then velocity vs. time, then acceleration vs. time.

Analysis (Part 1):

The timer strikes exactly 60 times per second, so the time for each 12 strikes must be 12/60 or 0.2 seconds. When filling out the table below, look at the displacements between each set of 12 dots. It might help to mark every twelfth dot (12^th, 24^th, 36^th, 48^th....etc.). Measure the total distance from thefirst dot to each of these marks (there will be maybe 6 or 8 dots), and fill in the first column of the table with these values, but be to use SI units! Use scrap paper if you need it to convert units. Also measure the displacement between each 12 dot interval and put that data in the second column below. Calculate the velocity during each interval from the displacement during that interval (column 2) and the time of that interval (0.2 sec). Again, use SI units.

Quickly make a rough graph of total displacement (column 1) vs. time, with displacement on the y axis and time on the x axis.

Put a little more effort into making a nice and precise graph of velocity (column 3) vs. time. Put velocity on the y axis, and time on the x axis. Axes must be labeled, with units!