Sonic+Ranger+Lab+2+Velocity+vs.+Time+Graphs


 * Lab Title:** Sonic Ranger Lab 2: Velocity vs. Time Graph


 * Primary Authors:** Jake Philip


 * Contributing Authors:** Peter, Kelsey
 * Abstract:** The goal of this lab is to get a better understanding of velocity and its relation to motion. Through this lab, we can get an idea of what a velocity-time graph visually looks like. We can see what motions cause the graph to form different lines. Along with this, we get a feel for position and its relation with velocity. Along with this, a goal in this lab is to Connect motions in the real world to velocity - time graphs.
 * Introduction/Backround Information:** In this lab, we will be using the Sonic Ranger and a program called Logger Pro. The Sonic Ranger emits sound pulses which reflect off of objects and travel back to it. At the same time that the Sonic Ranger is doing this, the Logger Pro program determines the distance of the object using the data from the Sonic Ranger and then put the data into a graph. Two graphs are made, a position-time graph and a velocity-time graph. For this lab we will be focusing on the velocity-time graph. While collecting data, you may find that you need the Logger Pro to collect for a longer period of time. In, order to do this you need to select 'Extend Collection" under the experiment menu. Throughout the lab, positive direction will be conidered, moving away from the motion detector.

Velocity will be defined as the time rate of change of position of a body in a specified direction. The formula for velocity is (displacement/time) or change in space/change in time.

Different graphs will be looked on and from there, students must experiment with different motions to see what motions cause what graphs. Then, a certain motion must be done and you must figure out the acceleration in the motion.

In the first part of the lab nine velocity-time graphs were given. Using The Sonic Ranger and the Logger Pro program, students were to replicate the nine graphs using a small plastic car. The Sonic Ranger was placed at the end of the desk and collected data as the students moved the car. The students had to figure out how the cars effected the graph that was produced. After the graphs were matched, they should have been described by the students, using words such as away, towards, increasing, decreasing, constant, slow, fast. In the second part the students were to use the same materials, but instead of replicating a graph that had already been made, the students were given a set of instructions of motion and had to make a graph according to these motions. The car was to move away at a constant speed, stop for a little, and move towards the detector at a constant speed. The graph was then to be printed out and using the graph, the students were supposed to find out the displacement during the away motion, the displacement during the towards motion, and the total displacement. The average velocity of the three must be found also. First, graphs with different lines were given. We must experiement with differient motions to figure out what motions cause what graphs.8 Motion: Moving away from the detector at a fast and constant speed. So the line has no slope and is farther from the x-axis. Motion: The car is moving away from the dectector again but this time it is moving at a slower and constant speed. The line is horizontal and slower to the x-axis. Motion: There is no movement, therefore, the line is neither above or below the line. Motion: The car is moving toward the motion detector at a slow constant speed. Thus making the line a straight line close to the x-axis. Motion: The car is moving toward the motion detector at a fast, constant speed. The line is parallel to the x-axis but farther away. Motion: This one is a little different since the line is no longer horizontal. The line has a constant positive slope above the x-axis. Thus the car is moving away while increasing its speed. Motion: The car is moving in a negative direction while decreasing speed Motion: The car is moving away from the detector, or in a positive direction, while decreasing speed. Therefore, the line is above the x-axis and has a negative slope because the car is deceasing speed. Motion: The car is moving in a negative directoin while increasing its speed. In this part, students are asked to job away from the detector as a constand speed then stop for a little while, then walk back to the motion detector at a slower speed. Then the graph was to be printed (See below). Then find the displacement when walking toward, joggin away and the whole trip. Then find the average velocity of the toward,away, and overall motion.
 * Method:**
 * Data:**
 * PART ONE**
 * Graph A**
 * Graph B**
 * Graph C**
 * Graph D**
 * Graph E**
 * Graph F**
 * Graph G**
 * Graph H**
 * Graph I**
 * PART 2**

Diplacement during away motion: Average Velocity is 0.6 m/s. Change in time is 1.1 seconds. So 0.6*1.1 = 0.66. Thus the displacement is 0.66 m. Displacement during the toward motion: We know that the car is coming back to its oringal locations o the displacement will be the same as the away motion but negative. -0.66 m. Overall Displacement: Since the car leave but comes back to its oringal location, the displacement is 0 meters. Velocity away: 0.6 m/s Velocity toward: -0.3 m/s Average velocity: (0.6-0.3)/2 = 0.15m/s Follow up Questions: 1.) How is positive velocity distinguished from negative velocity on a velocity-time graph?
 * Results:**

Positive velocity is above the time axis while negative velocity is below the time axis. 2.) How is a high speed distinguished from a low speed on a velocity-time graph? If the line is far from the time axis then we know it has a higher speed, but if it is closer to the time axis, then we know that is has a lower speed.  3.)What other interesting connections can you make between your motion and the velocity-time graph? The velocity-time graph can be connected to a workout graph. The high flat line is like an intense workout for a long time. The diagnol line is like a warm up that is increasign in intensity. And the lines below the time axis can be like eating unhealthy because thats a negative to the workout.

Through this lab we learned what movements cause certain types of velocity-graphs. If one moves the car away from the detector at a constant speed, then the graph will be a straight line above the time axis. The distance from the time-axis depends on constant speed. If the car moves toward the detector at a constant speed, then the graph will be a straight line below the time axis. A similar thing would occur if the car moves away from the detector. They only difference would be that the straight line would lie above the time axis. If the car is moving away or toward at an increasing or decreasing speed, then the line will be diagnol with a constant slope. The steeper the slope, the faster the car is speeding up. This can be related to the position graphs. When a car is increasing speed, the position-time graph has a concave up shape to it. If the slope of that function was taken it and applied to the velocity-time graph, then we would end up with a diagnol graph. When the position-time graph has a negative slope and changing speed, then the velocity-time graph will have a negative slope. If the line is on the time axis, then we know that there is no movement.
 * Conclusion:**

We can connect this to the real world because we now visually know what each graph looks like in movements. A specific real world connection that can be made with velocoty-time graphs is workout graphs.