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LINEAR MOTION Chapter 4

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Puzzler QUESTION: Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you, and the other is 3 meters upstream from you. Which can you swim to in the shortest time? The preserver upstream The preserver downstream Each swim requires the same time. downstream

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Puzzler Answer ANSWER: C To get a grip on this, pretend that you are in a swimming pool on a fast-moving ocean liner. If both life preservers are the same distance from you in the pool, swimming toward either would take the same time. The speed of the liner through the water makes no difference, just as it makes no difference to people playing shuffleboard or billiards. Can you see that, in the flowing river, you're like a person in a pool aboard a moving ocean liner—that swimming toward either preserver takes the same time? All objects have uniform motion; they are all in (dynamic) equilibrium.

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**One-Dimensional Motion and Distance**

Motion in one dimension refers to straight-line motion (Linear) Example: train traveling on a straight track

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**Motion and Frame of Reference**

a change in position Frame of reference A point against which position is measured Example: A train traveling between stations It is in motion when measured against the track. It is stationary when measured against a seat. Tell students that generally, the frame of reference we use is Earth. This is why many students said that the book was not in motion (for the previous slide).

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**DETECTING MOTION RELATIVE MOTION**

In order to see an object in motion, you need to compare it to a frame of reference, such as a stationary background. RELATIVE MOTION

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**RELATIVE MOTION WEB SITES**

Determine the displacement and distance for the journey illustrated below. 120 m north, 57 m south, 5 minute rest, 78 m south, 40 m north, 67 m north, 99 m south, 7 minute rest, 42 m north.

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**Displacement (x) vs. Distance (d)**

5 m = 17 m Displacement means straight line distance from the initial position to the final position (change in position) Distance means the total length of the path traveled by an object. 7 m 5 m Keep in mind that distance is the addition of all lengths of the path traveled by an object in all directions.

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Think: How is it possible for a car to travel a distance of 5 miles, and have a displacement is equal to zero. Drive around a very long block and return to the starting position. Back out of your garage, drive 5 miles, and return to your garage.

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**Average Velocity Average speed equation is written v = d/t**

Average velocity is total displacement divided by the time interval during which the displacement occurred. As equations are written, show students how units for each quantity can be deduced from the equation. Have students determine the SI units before moving forward in the slide. This technique limits the amount of memorization required. See if students can suggest additional possible units of average velocity. Average speed equation is written v = d/t v is average speed t is time d is distance

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**Average Velocity The units can be determined from the equation.**

Section 1 Displacement and Velocity Chapter 2 Average Velocity The units can be determined from the equation. SI Units: meters per second or m/s Other Possible Units: mi/h, km/h, cm/year

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**Classroom Practice Problems**

A car travels 36 km to the north in 30.0 min. Find the average velocity in km/min and in km/h. Answer: 1.2 km/min to the north or 72 km/h to the north A car travels km to the east. If the first half of the distance is driven at 50.0 km/h and the second half at a km/h, what is the average velocity? Answer: 66.7 km/h to the east For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow them some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful. Show students how to obtain both answers to the first problem. For the second problem, point out the error in simply averaging the two velocities. This is wrong because the car spends more time traveling at the slower speed.

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Constant Velocity Object maintains the same speed in the same direction Example: Car travels at 35 km/h due east These same sign conventions will apply to velocity, acceleration, force, momentum and so on.

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**Speed Speed does not include direction while velocity does.**

Speed uses distance rather than displacement. In a round trip, the average velocity is zero but the average speed is not zero. When discussing the second bullet point, ask students to describe the difference between distance and displacement. Then, ask students to explain why the third bullet point is true. (Answer: In a round trip, the displacement is zero, thus the average velocity is also zero. The speed is not zero because the distance traveled is not zero.)

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Velocity and Speed Velocity describes motion with both a direction and a numerical value (a magnitude). Speed has no direction, only magnitude.

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**Graphing Motion Position (distance) vs. Time Graphs**

At rest, no change in position

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**Graphing Motion Position (distance) vs. Time Graphs**

The objects shown by the yellow and blue lines are covering equal amounts of distance in equal amounts of time. The velocity of the object can be calculated by evaluating the slope of each line, or one point along each line. Yellow line (constant speed of 3 m/s) Blue line (constant speed of 1 m/s)

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**Graphing Motion Position (distance) vs. Time Graphs**

The object represented by the yellow line is covering a greater amount of distance with each unit of time that passes. (it is speeding up) Changing distance over time or acceleration.

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**Graphing Motion (position vs. time)**

What type of motion does this graph show? Answer: Constant speed (straight line) What is the slope of this line? Answer: 1 m/s What is the average velocity? Remind students that slopes have units. Many might just say that the slope is “1” instead of “1 m/s.”

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**Graphing Motion Describe the motion of each object. Answers**

Object 1: constant velocity to the right or upward Object 2: constant velocity of zero (at rest) Object 3: constant velocity to the left or downward Have students write their answers in their notes. Discuss the answer to object 1 before they answer questions 2 and 3. Many students will forget that velocity includes direction so they might simply answer “constant velocity” or “constant forward velocity”. This offers a chance to review the sign conventions for displacement and velocity.

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Puzzler QUESTION: Would this situation change if the life preservers were fixed in place relative to the swimmer and the river’s current? Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you, and the other is 3 meters upstream from you. Which can you swim to in the shortest time? The preserver upstream The preserver downstream Each swim requires the same time.

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**HOW CAN YOU TELL THAT AN OBJECT IS MOVING?**

THE MOTION OF ONE OBJECT MAKES SENSE ONLY WHEN IT IS COMPARED TO ANOTHER OBJECT THAT HAS A DIFFERENT MOTION.

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SENSING MOTION We cannot sense uniform motion (mechanical equilibrium) unless we can compare our motion to an object with different motion. We can only sense changes in uniform motion, which is acceleration.

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**THE FATHERS OF MOTION: Falling Objects**

Aristotle (~300 BC) hypothesized that heavier objects fell faster than lighter objects. Galileo (~1500’s) tested Aristotle’s hypothesis about falling objects and proved it wrong. Sir Isaac Newton (late 1600’s) extended Galileo’s work into three laws of motion and the universal law of gravitation. Newton showed that the universe ran according to natural laws.

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One Dimensional Motion

One Dimensional Motion

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