Date
Page # / Uniform Motion(K)
9/3/2013
6-7
Seed Question
(Individual, then discuss as whole class) / Describe a real-life situation in which motion might be considered uniform. Use at least 2 complete sentences.
Exploration
(With a partner)
25 minutes / Read the first two sections of “Quantitative Descriptions of Positions and Times.” Then complete the following exercises in your PJ.
Exercise 2.1
On your own paper, calculate for the figure above and show your work. What does the sign of tell you about the motion?
Exercise 2.2
On your own paper, calculate the displacement for each of the following motions. For each case, is the first position and is the later position. Draw an arrow on your paper to represent the direction of the displacement for each.
Exercise 2.3
Which quantity tells you where an object is located, or ?
(If an object keeps moving in the same direction, is the distance the object moves. If the object turns around, however, the distance it travels is greater than . (The symbol means the absolute value of . Consult your teacher if you are not sure what absolute value means.)
Copy the diagrams above into your PJ. Develop a definition for , , and .
Now continue reading “”Starting Positions” and complete the following exercises in your PJ.
Exercise 2.4
Two students conduct an experiment in which an object is moved from position to position. Student 1 and student 2 each place a meter stick next to the line of motion, as shown below.
What value would student 1 measure for ? What value would student 2 measure for ?
What value would student 1 measure for ? What value would student 2 measure for ?
What value would student 1 give for ? What value would student 2 give for ?
Now continue reading “Time” and complete the following exercises in your PJ.
Exercise 2.5
Two observers timed the motion of a car from one place to another. The first observer’s clock read 262 seconds at the start and 375 seconds at the end of the car’s motion. The second observer’s clock read -86 seconds at the start. What did it read at the end?
Exercise 2.6
Tell whether the answer top each of the following questions would be a time or a duration.
A. When will we go shopping?
B. How long will it be before the bus comes?
C. When did his term in office end?
D. How old is that building?
E. When the war ended, how long had you been overseas?
F. How much time does a job like that take?
The term instant needs special attention because its meaning is physics is not quite the same as it is in ordinary language. In physics, an instant is always a time, never a time interval. An instant is a when, not a how long. The phrase at an instant means the same sort of thing as at 2:15.
Big Ideas
(Whole class)
20 minutes to discuss and collaborate. / Describing motion, some things to talk about:
Position/Change in Position/Starting Position/Reference Point
Distance/Displacement
Scalar/Vector/Magnitude
Time/Duration
For Further Contemplation / Questions or comments? Pick-up “Uniform Motion” for homework. DUE TOMORROW!
Quantitative Descriptions of Positions and Times (K)
Position
Whenever an object moves along a straight line, it is possible to imagine a meter stick lying alongside the path of the object. We can imagine this meter stick is extending forever in both directions. The meter stick represents a coordinate system.
We can describe where an object is by stating the number that is closest to it along the meter stick. This number is called the position of the object. We use the symbol x to represent position. In the figure above, the square is next to the +2 cm mark, so it has a position of +2 cm. Using the symbol x, we would say that x = 2 cm for the square. For the circle, x = -3 cm.
Displacement
If an object moves from an initial position (xi) to a final position (xf), the difference between these numbers (xf - xi) is called the displacement or the change of position of the object. We will use the symbol for : where is read “delta x.” We always use the Greek letter delta (∆) to mean final value minus initial value. Thus the symbol ∆ represents the change in a quantity.
A displacement is often represented by an arrow drawn from the initial position to the final position. The length of the arrow represents how far the final position is located from the initial position, and the arrowhead shows the direction of motion. An arrow representing displacement is shown in the following figure.
Starting Positions
Motion may begin at any position number. Often is defined to be the place where the motion begins, but this is not necessary. Consider the following example:
A farmer lives between two large cities, A and B. The highway that passes the farm is marked with mileposts. The numbering system starts at city A and continues on to city B. The farm is located at milepost 198. Consider a trip the farmer took into the nearby small town at milepost 206. Her initial position according to the highway mileposts was not 0, since she did not start her trip at city A. Her initial position was mi, and her final position was mi. The farmer might live her entire life without ever going to city A. In that case, her position would never be 0.
We will frequently encounter situations like the case above, where the motion does not start at . The choice of the location for is arbitrary; however, once the choice has been made for a particular problem, it should not be changed. The location where the position is zero is often called the reference point of the coordinate system. The following exercise illustrates how the choice of the reference point affects position and displacement measurements.
Time
The word time has several meaning in ordinary language. For example: What time did he arrive? How much time does that job take? We had a fine time. Time out. Our time has come. In physics, the word time must be used carefully because it is used to name several quantities. The exact meaning of the word in physics is often told in the words that go with it, for example, at that time, for a long time. We will be concerned with two uses of the word corresponding to two different quantities: one called the time, meaning a clock reading, and the other called duration, time interval, or amount of time. These quantities are discussed below.
In describing positions, we imagine a meter stick that continues forever in both directions. When considering time, we imagine a clock that will continue to run forever. Instead of an ordinary clock, we imagine a clock that just keeps count of seconds. It does not start over after 12 hours as our usual clocks do. The clock we imagine keeps counting up to millions and billions of seconds. We use the symbol to represent the clocks reading.
The number on the clock is called the time. We describe when something happens by giving the time shown in the clock (the clock reading) as the event occurs. A typical event, for example, would be passing of the 10 cm mark by a moving object. If the clock read 25 seconds as this happened, we would day that at .
Just as is not necessarily a special place, is not necessarily a special instant. In particular, does not have to be the instant that motion begins. For example, suppose two cars are making the same trip but one of them has a 5-minute head start. We might set out clock to read when the first car starts, but the second car’s motion would begin at .
Instants before have negative time numbers, such as . This is similar to what we do for years before the year one, such as 1026 B.C. Negative times are perfectly ordinary; they are just earlier than positive times.