Motion
This unit focused on the motion of an object, which can be shown or measured in many different ways. All of these have different equations and types of graphs that go with them to represent the motion of the object. These different forms of motion are velocity/speed and distance/displacement/position.
Velocity
The velocity of an object is the change in distance over the time. An object can have multiple different velocities over a certain period of time, and an object can have a negative or positive velocity. A positive velocity is when the object is moving forward, or away from the origin. For negative velocity the object could be going the same speed, but just backwards or towards the origin. The average velocity is found by taking the change in x over time. Velocity is unique because it can be shown using all three types of graphs we have learned about; a position vs time graph, a velocity vs time graph, and a motion map. The equation for average velocity is V=change in position/time.
Shown above is a position vs time graph. Velocity is demonstrated in this graph because the velocity is the slope of the line, or the position over the time, because velocity shows how far something goes in however much time. The average velocity would just be the change in position over a given time over that time. If the line goes flat the object is standing still.
This is a velocity vs time graph. It only shows the velocity and the time, and position can not be found out from this. The velocity is on the y axis and the time is the x axis. Where ever the line is on the y axis is what the velocity is and how far it goes across the time is how long it goes for. It can fluctuate by going up and down with speeds. If it goes in the negative that means the object started moving in the opposite direction. If it is at 0 velocity that means the object is standing still.
Above is a motion map. A motion map is most commonly used to display position, but velocity can be seen in it. Each dot represents 1 second, and the line below is usually labeled with numbers which represent position. The lines coming off of the dots show the velocity. The longer lines mean the object is moving faster and the shorter the lines are the slower the object is moving. When there are dots going down below each other with no lines that is when the object is standing still. When the lines move in an opposite direction of the beginning ones it means that the object has a negative velocity and is moving backwards.
Speed
Speed is different from velocity. While velocity shows the change in position over the time and shows the direction speed simply shows how fast an object is moving and is based on the path length. Speed is shown in a position vs time graph.
Distance
The distance of an object is how far it went not how far it got. For example a car can drive in a circle for an hour and drive a total of 60 miles but actually go 0 feet. The distance is the 60 miles. It is the total path length on a position vs time graph.
Position
Position is more commonly used in physics than distance because position shows the actual location of an object. The equation of a line is position=(velocity)(time) + starting position. This can be used to find all aspects of an object's motion, and it is very easy to find position this way because it is already set up to do that. A position vs time graph shows the position on the y axis, and a motion map shows the position on the number line.
Displacement
The displacement is the final position compared to the starting position, or how far the object got from the starting position. Even if an object goes 100 miles away from the starting position if it ends up where it started the displacement is 0. Displacement can be found in 2 ways. One is to the final position (x final) and subtract the starting position (x initial). Another way is to use a velocity vs time graph. If you take the area of a section of a velocity vs time graph that is the displacement. This means multiplying the velocity on the y axis by however much time you are measuring for on the x axis.
Connections to the Real World
This unit is extremely prevalent in daily life. Most objects we encounter have a motion to them. Cars for example are an object designed to have motion. We see motion all the time and understanding it's elements can help us manipulate it. In math these formulas can be used to solve many problems, especially ones pertaining to objects passing each other. Using the formulas for velocity and position we can make accurate predictions about objects and where they are going.
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