Velocity!

Walking Lab

This lab involved one person in our lab group walking to the left and right of a starting position based on how many meters he or she was supposed to move per second. The number of meters travelled per second, also known as velocity, was given to us in the form of a graph. We chose 0m as our starting position, and movement to the left of the origin was considered negative, while movement to the right of the origin was considered positive.

Data:

To achieve the data, we made a chart, so we could write data for time (in seconds), position (in meters), and velocity (in meters per second). We put the seconds in increments of one (like the given vt graph had) and then began writing the numbers from the v-axis of the vt graph that corresponded with our t-values in the chart down. The velocities were placed between the seconds since the V number represents the number of meters moved per second between the t-value and the second prior. Once we finished that, we gave our t-value of 0s a position of 0m to act as the starting point. We then subtracted the velocity from the previous position value in order to finish the data chart.

XT Graph:

We chose 0m as our starting position on the graph and then began using the values of the vt graph to give us the slopes of the line segments in the xt graph. Once we plotted points the correct number of units away (which the vt graph told us by way of the v-values), we connected the points from left to right with straight line segments.


VT Graph:


Given.








Motion Map:



We chose 0m as the starting point as we had done for the data and xt graph. We drew a horizontal line to represent position, and added dashes that each represented one meter. We started at 0m and drew a line to the left since the velocity was negative, and the arrow spanned two units since that was the distance it traveled in the first second (2 meters). We continued putting dots for each second from the corresponding points on the xt graph, and the arrow changed direction every time velocity changed from - to + or + to -. Dots represented seconds, and therefore any dot without an arrow connected represented no motion for that second.


(a) Finding total distance from 0s to 5s:

|-2m| + |-2m| + |1.5m| + |.75m| + |0m| = 6.25m

To find the total distance, we added the absolute value of each number of meters that the person moved since "total distance" encompasses the entire amount of motion that was done. We do not include the distance that was travelled between 5 and 8 seconds, however, since the directions specifically ask for the total distance from 0s to 5s.


(b) Finding total displacement from 0s to 5s:

-2m + -2m + 1.5m + .75m + 0m = -1.75m

To find the total displacement, we add up each distance that was travelled in the span of one second. This time, we do not use absolute value signs because we want to see where the person ended up in relation to where they started, rather than the total distance that they moved.  You may notice that these numbers are the same as the ones in the velocity column of our data table: that is correct. The reason that the unit is just m (rather than m/s) is that each of these numbers represent the distance that the person went in 1s. Again, remember that we are only looking at the numbers from 0s to 5s.


(c) Finding average speed from 0s to 5s:

speed = distance / time = 6.25m / 5s = 1.25m/s

In order to find average speed, we must use the total distance that we found earlier, as well as the time period that we are given. In part a, we found that the total distance was 6.25m. To find time, we merely subtract 0s from 5s. Then, we plug these into the formula speed equals distance divided by time. We then find that the average speed from 0s to 5s is 1.24m/s.


(d) Finding average velocity from 0s to 5s:

velocity = displacement/time = -1.75m/5s = -.35m/s

To find velocity, we must know displacement and time. We found that the displacement is -1.75m in part b, and the time is still 5s. Therefore, when we plug those numbers into the equation velocity equals displacement divided by time, we find that the average velocity from 0s to 5s is -.35m/s.