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Concepts of Motion

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Concepts of Motion

Mr. Wilt

Appoquinimink high School

Motion is the change of an object’s position with time. Examples of moving objects include bicycles, baseballs, cars, airplanes, and rockets.

The path along which an object moves, be it a straight path or a curved path, is called the object’s trajectory.

Imagine you had a camera in a fixed position as an object moves by. The camera could be set to take snapshots at equally spaced instants of time.

If you were to stack these snapshots on top of each other, the composite photo would be a motion diagram.

When dealing with objects moving along a trajectory, it can be useful to treat the object as if it were just a single point, without size or shape. Likewise, we can treat the object as if all of its mass were concentrated into this single point.

An object that can be represented as a mass at a single point is called a particle. A particle has no size, no shape, and no distinction between top and bottom or between front and back.

This simplification of reality is called a model.

Models allow us to focus on the important aspects of a phenomenon by excluding those aspects that play only a minor role.

The particle model of motion is a simplification in which we treat a moving object as if all of its mass were concentrated at a single point.

The location of an object at a particular instant in time is called the object’s position.

If a friend calls to ask where you are, you might reply that you are 4 miles east of the post office.

First, you had to give a reference point (the post office). We call this fixed reference point the origin.

Second, you needed to give how far you were from the origin – in this case, 4 miles.

Finally, you needed to give some information on the direction of your position in reference to the origin.

We’ll need these same three pieces of information in order to specify any object’s position along a line.

The origin is the point from which you will measure the position to the object.

The placement of the origin is arbitrary and you can place it wherever you’d like.

Lay down an imaginary axis along the line of the object’s motion. The axis should be marked off in equally spaced divisions of distance.

Place the zero mark at the origin. This allows us to locate the object by placing it at a specific distance from the origin.

Imagine the axis extending out from opposite sides of the origin. On one side, the marks are increasingly positive; on the other side, the marks are increasingly negative.

Depending on whether an object’s position is reported as positive or negative, we know on which side of the origin the object is.

By placing an origin and an axis marked in both the positive and negative directions, you have created a coordinate system.

- We will use a symbol such as x or y to represent the position along the axis.
- For instance, we can say, “the cow is at x = -5 miles.”

Each image or frame in a motion diagram should be labeled to indicate the time, as read from a clock or stopwatch.

You must make the choice as to which frame you assign to be t = 0.

Like placing an origin, this choice is arbitrary, but it is often convenient to choose the beginning of the relevant motion to be labeled “t = 0 seconds.”

Now that we can appropriately measure position and time, we can describe motion by measuring the changes in position that occur with time.

- Consider the following:
- Sam is standing 50 feet (ft) east of the corner of 12th Street and Vine. He then walks to a second point 150 ft east of Vine. What is Sam’s change of position?

Since the origin was placed at the intersection, we can see that Sam’s final position is xf = 150 ft, indicating that he is 150 feet east of the origin (positive number indicates the direction is east of the origin).

Sam has changed position, and a change of position is called a displacement.

His displacement is labeled Δx in the diagram. The Greek letter delta (Δ) is used to indicate the change in a quantity. Δx indicates a change in the position x.

Generally, the change in any quantity is the final value of the quantity minus the initial value.

Displacement is the difference between the final position xf and an initial position xi.

The positive sign of the displacement indicates that Sam moved 100 ft to the right along the x-axis, or 100 ft east.

If Sam had moved from his initial position to the origin, his displacement would have been

The negative sign indicates that Sam moved 50 ft to the left along the x-axis, or 50 ft west.

To quantify motion, we’ll also need to consider changes in time, which we call time intervals.

The diagram above shows the motion of a bicycle as it moves from left to right at a constant speed.

The displacement between xi and xf is

Similarly, the time interval between these two points is

*Note that Δt will always be positive because tf is always greater than ti.

An object moving along a straight line at a constant speed is neither speeding up nor slowing down.

This motion at a constant speed is called uniform motion.

For an object in uniform motion, successive frames of the motion diagram are equally spaced. Δx is the same between successive frames.

An object’s speed is defined as the ratio of the total distance an object travels in a given time interval divided by the time interval.

- Because speed is only concerned with the total distance, “distance traveled” doesn’t give us any information about the object’s direction. Therefore, assuming the distance is non-zero, speed can only be a positive quantity.

While “distance traveled” doesn’t give us any information about the direction that an object is traveling, we have seen that displacement does contain this information.

We can now define a new quantity, the average velocity, as

This diagram shows two bicycles traveling at the same speed, but with different velocities.

Let’s take a look at computing the velocities of the two bikes using the 1 second time interval between the t = 2 s and t = 3 s positions for each bike.

Bike 1:

Bike 2:

*Note: The subscripts here represent the time at which each position is reached. They still represent the final quantity minus the initial quantity for the motion with which we are concerned.

The two velocities have opposite signs because they are traveling in opposite directions.

Speed measures only how fast an object moves, but velocity tells us both an object’s speed and its direction.

A positive velocity indicates motion to the right or, for vertical motion, upward. Similarly, an object moving to the left, or down, has a negative velocity.

Much of the content of this presentation, including diagrams, is adapted from College Physics: A Strategic Approach, 3rd edition by Knight, Jones, and Field.

All content is used for the sole purpose of education.