course Phy 121 •G²Âµ¹ÃÙ‡ÒÉÜ“‚p“ª†²ï®¥ô’µˆˆassignment #002 002. Velocity Physics I 06-10-2008
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19:19:27 `q001. Note that there are 14 questions in this assignment. If an object moves 12 meters in 4 seconds, then at what average rate is the object moving? Explain how you obtained your result in terms of commonsense images.
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RESPONSE --> 3m/sec. I divided 12 meters by 4 seconds. confidence assessment: 2
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19:20:06 Moving 12 meters in 4 seconds, we move an average of 3 meters every second. We can imagine dividing up the 12 meters into four equal parts, one for each second. Each part will have 3 meters, corresponding to the distance moved in 1 second, on the average.
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RESPONSE --> My answer was a lot shorter, but I understand. self critique assessment: 2
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19:21:34 `q002. How is this problem related to the concept of a rate?
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RESPONSE --> Rate has to do with how long it takes for something to occur. It took an average of 3m/s on the problem. We can judge things by rates. How fast or slow something is moving. confidence assessment: 2
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19:21:47 A rate is obtained by dividing the change in a quantity by the change in another quantity on which is dependent. In this case we divided the change in position by the time during which that change occurred.
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RESPONSE --> ok self critique assessment: 2
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19:23:17 `q003. Is object position dependent on time or is time dependent on object position?
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RESPONSE --> Either one. You can figure out position or time of you have the other variables. You could solve for position with respect for time or time with respect for position. confidence assessment: 1
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19:23:54 Object position is dependent on time--the clock runs whether the object is moving or not so time is independent of position. Clock time is pretty much independent of anything else.
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RESPONSE --> Ok. I understand, the clock always runs, the object doesn't. self critique assessment: 2
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19:24:46 `q004. So the rate here is the average rate at which position is changing with respect to clock time. Explain what concepts, if any, you missed in your explanations.
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RESPONSE --> I missed that things are dependent on clock time because it's always running. The object will have to start and stop sometime. confidence assessment: 2
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19:25:05 You should always self-critique your work in this manner. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.
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RESPONSE --> ok self critique assessment: 2
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19:26:46 `q005. If an object is displaced -6 meters in three seconds, then what is the average speed of the object what is its average velocity? Explain how you obtained your result in terms of commonsense images and ideas.
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RESPONSE --> The average speed should be -2m/sec. If an object rolls -6m in 3 seconds then the velocity is the change in distance/change in time. confidence assessment: 2
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19:29:10 Speed is the average rate at which distance changes, and distance cannot be negative. Therefore speed cannot be negative. Velocity is the average rate at which position changes, and position changes can be positive or negative.
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RESPONSE --> Ok, I think I've got it. Even though the object rolled maybe backwards, it still rolled 6 m, whichever way. The position change is -6m but the average velocity is 2m/s self critique assessment: 2
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19:30:47 `q006. If `ds stands for the change in the position of an object and `dt for the time interval during which the position changes, then what expression stands for the average velocity vAve of the object during this time interval?
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RESPONSE --> vAve = 'ds/'dt confidence assessment: 2
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19:31:00 Average velocity is rate of change of position. Change in position is `ds and change in clock tim is `dt, so vAve = `ds / `dt.
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RESPONSE --> correct self critique assessment: 2
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19:31:50 `q007. How do you write the expressions `ds and `dt on your paper?
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RESPONSE --> Exactly like you do on here. I have on occasion used the delta symbol. confidence assessment: 2
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19:32:28 You use the Greek capital Delta symbol Delta. `d is often used here because the symbol for Delta is not interpreted correctly by some Internet browsers. You should get in the habit of thinking and writing Delta when you see `d. You may use either `d or Delta when submitting work and answering questions.
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RESPONSE --> Is the Delta symbol like a triangle? self critique assessment: 2
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19:35:49 `q008. If an object changes position at an average rate of 5 meters/second for 10 seconds, then how far does it move? How is this problem related to the concept of a rate?
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RESPONSE --> It moves 50m. 5m/s = 'ds/10sec. Again, we know the rate and how long it took so we can figure out how far the object went. confidence assessment: 2
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19:37:13 In this problem you are given the rate at which position changes with respect to time, and you are given the time interval during which to calculate the change in position. Given the rate at which one quantity changes with respect to another, and the change in the second quantity, how do we obtain the resulting change in the first?
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RESPONSE --> to find the change in position, you would multiply th velocity * change in time interval self critique assessment: 2
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19:38:45 `q009. If vAve stands for the rate at which the position of the object changes (also called velocity) and `dt for the time interval during which the change in position is to be calculated, then how to we write the expression for the change `ds in the position?
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RESPONSE --> 'ds = vAve * 'dt confidence assessment: 2
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19:39:00 To find the change in a quantity we multiply the rate by the time interval during which the change occurs. We therefore obtain the change in position by multiplying the velocity by the time interval: `ds = vAve * `dt. The units of this calculation pretty much tell us what to do: Just as when we multiply pay rate by time (dollar / hr * hours of work) or automobile velocity by the time interval (miles / hour * hour), when we multiply vAve, in cm / sec or meters / sec or whatever, by `dt in seconds, we get displacement in cm or meters, or whatever, depending on the units of distance used.
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RESPONSE --> ok self critique assessment: 2
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19:41:32 `q010. Explain how the quantities average velocity vAve, time interval `dt and displacement `ds are related by the definition of a rate, and how this relationship can be used to solve the current problem problem.
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RESPONSE --> To find any of the rates, we must know 2 of the following three: how far an object traveled, how long it took to get there, or the average velocity. These numbers allow us to find how fast or slow an object is moving. confidence assessment: 1
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19:41:52 vAve is the average rate at which position changes. The change in position is the displacement `ds, the change in clock time is `dt, so vAve = `ds / `dt.
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RESPONSE --> yes self critique assessment: 2
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19:45:30 `q011. The basic rate relationship vAve = `ds / `dt expresses the definition of average velocity vAve as the rate at which position s changes with respect to clock time t. What algebraic steps do we use to solve this equation for `ds, and what is our result?
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RESPONSE --> To find 'ds in this equation we need to multiply both sides of the equation by 'dt to get the answer. By multiplying ('ds/'dt) by ('dt) the 'dt's cancel out and all that's left on that side is 'ds. vAve * 'dt = 'ds confidence assessment: 2
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19:45:43 To solve vAve = `ds / `dt for `ds, we multiply both sides by `dt. The steps: vAve = `ds / `dt. Multiply both sides by `dt: vAve * `dt = `ds / `dt * `dt Since `dt / `dt = 1 vAve * `dt = `ds . Switching sides we have `ds = vAve * `dt.
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RESPONSE --> correct self critique assessment: 2
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19:49:06 `q012. How is this result related to our intuition about the meanings of the terms average velocity, displacement and clock time?
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RESPONSE --> This is really not too hard to figure out. Most of us can figure things like miles per hour or how far we walk in a certain amount of time. These terms we use are more ""mathmatical"". When you think about it, many of us do this in everyday life. Gas mileage, how far we can travel in a certain amount of time, etc. confidence assessment: 1
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19:49:27 Our most direct intuition about velocity probably comes from watching an automobile speedometer. We know that if we multiply our average velocity in mph by the duration `dt of the time interval during which we travel, we get the distance traveled in miles. From this we easily extend the idea. Whenever we multiply our average velocity by the duration of the time interval, we expect to obtain the displacement, or change in position, during that time interval.
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RESPONSE --> I understand. self critique assessment: 2
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19:51:13 `q013. What algebraic steps do we use to solve the equation vAve = `ds / `dt for `dt, and what is our result?
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RESPONSE --> This is much like solving for 'ds. You would multiply both sides by 'ds and get 'dt = vAve * 'ds. confidence assessment: 2
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19:56:02 To solve vAve = `ds / `dt for `dt, we must get `dt out of the denominator. Thus we first multiply both sides by the denominator `dt. Then we can see where we are and takes the appropriate next that. The steps: vAve = `ds / `dt. Multiply both sides by `dt: vAve * `dt = `ds / `dt * `dt Since `dt / `dt = 1 vAve * `dt = `ds. We can now divide both sides by vAve to get `dt = `ds / vAve.
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RESPONSE --> I understand a litle better. I took notes on this and will review. self critique assessment: 2
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19:59:55 `q014. How is this result related to our intuition about the meanings of the terms average velocity, displacement and clock time?
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RESPONSE --> The change in time is equal to the change in position / the average velocity. We can use a common example of travel. If we change our car position by going 60 miles down the road and our average speed was 60 m/hr, then we find an hour has elapsed on the clock. confidence assessment: 1
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20:00:14 If we want to know how long it will take to make a trip at a certain speed, we know to divide the distance in miles by the speed in mph. If we divide the number of miles we need to travel by the number of miles we travel in hour, we get the number of hours required. We extend this to the general concept of dividing the displacement by the velocity to get the duration of the time interval.
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RESPONSE --> understood self critique assessment: 2
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