Unit Summary Blog Post

This unit I learned how to analyze velocity vs time graphs, position vs time graphs, average velocity, average speed, motion maps, and how to determine displacement and instantaneous velocity. Most importantly, I learned how to interpret a graph simply by having one or more of these solutions. For example:

After receiving this information, I can construct a velocity vs. time graph and a position vs. time graph:

Velocity, Average Velocity & Speed
Velocity is equivalent to change in x over change in t. Average velocity is found by dividing distance traveled over time elapsed. Velocity is defined as the rate at which an object changes its position, but should not be confused with speed. Speed does not have a direction, while velocity does (scalar vs. vector). Speed refers to how fast an object is moving, while velocity refers to the rate at which an object changes position in a specific direction. Speed is calculated by dividing distance over time. Say you are driving in your car and the speedometer reads 45 mph. This means that after driving an hour at the same speed, you will have traveled 45 miles. Say you drove 200 miles on a race track in 2.4 hours, one can calculate the average speed: 200 m/2.4 hr=83.3 mph. For velocity, we find that you have a displacement of zero, as the start and finish line on the track is the same. Therefore, we can find average velocity: 0 m/2.4 hr=0 mph. This is a clear example of when speed and velocity can be different, as I struggled with comprehending how an object could have a high speed but a velocity of zero.


Linear Graphs
The two graphs we use the most in physics are velocity vs. time graphs and position vs. time graphs. These are helpful visual representations of an object's movement over a certain period of time. Here is an example of a velocity vs. time graph on the left and a position vs. time graph on the right:

As you can see, since the velocity of the object was constant throughout the p vs t graph, the line was straight on the v vs. t graph, signifying a constant, unchanging velocity. If the object were moving negatively, or towards the origin, the v vs. t graph would drop below the x axis, indicating a negative velocity. When an object has a constant velocity, the line is always straight on a velocity vs. time graph.

Motion Maps

Motion maps are a useful way to show the relationship between velocity and time. Each second is represented by a black dot and the length of an arrow shows how fast the object travels. Here is an example of a motion map: 

In this example, the object moves at a constant velocity to the right, stops for two seconds, changes direction and moves to left at a slower velocity than it initially did. 

Displacement & Distance 

In the image above, displacement is calculated by finding the distance between the origin and the final position (A and B). Say you walked 400 ft from point A to point B, this would be your distance. However, from Point A (origin) to point B (final position) in a straight line it is only 150 ft. Displacement can be calculated by= X final - X initial

Graphing Intersections

In the buggy lab we predicted the point of intersection for two buggys. My group's buggy started 200 cm away from the origin and the other group's buggy started -230 cm away. 

Buggy A: x= -30t + 200

Buggy B: x= 43.84t - 230

In order to calculate the predicted intersection point, we set the equations equal to one another and got: -30t +300=43.84t -230. We solved for t and received a predicted intersection time of 5.75 seconds. In order to find the position in which the buggys would meet, we plugged 5.75s in for t to solve for the point. It was predicted that Buggy A and Buggy B would meet at 27.6 cm north of the origin. 

****Important formulas:

x=(v)(t)=Xo
position=(velocity)(time) + starting position
slope= (ΔY) / (ΔX) which is also equal to the velocity of an object
displacement= X final - X initial 
velocity= position/time

Dependent & Independent variables
x axis: independent variable (control)
y axis: dependent variable (what we measure)

Part B
Physics is used in every day life, whether it is consciously recognized or not. In a cross country meet, the distance I run from the origin to the finish line is 3.1 miles. However, in reality the displacement between point A and point B is approximately 400 m at the ACA course. I use physics on a daily basis and do not even acknowledge it.