course Phy 231 J{Rb s{pϹassignment #002
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16:29:15 `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 --> The object moves at the average rate of 12m/4s = 3m/s. On average, the object moves 3meters every second, so at 1s, the distance will be 3m, at 2s, the distance will be 6m, at 3s, the distance will be 9m, and at 4s, the distance will be 12m. confidence assessment: 3
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16:29:25 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 --> self critique assessment: 3
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16:30:48 `q002. How is this problem related to the concept of a rate?
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RESPONSE --> This problem is related to a rate because we are looking for the average rate of change in the position of the object. confidence assessment: 3
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16:31:26 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 --> I could have mentioned that it was the rate of change in position relative to time. self critique assessment: 2
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16:32:06 `q003. Is object position dependent on time or is time dependent on object position?
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RESPONSE --> The position is dependent on time. confidence assessment: 3
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16:32:57 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 --> I could have described clock as being independent of anything else. self critique assessment: 2
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16:34:52 `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 --> In previous explanations I did say that the rate that we are talking about is the average rate at which position changes, but I did not specify with respect to clock time, which I should have. confidence assessment: 3
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16:35:12 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 --> self critique assessment: 3
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16:40:21 `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 --> In this case, the object is dispaced -6 meters which means that rather than moving in an opposite direction to what it was previously. -6m/3s = -2m/s In this case, in the first second, the object moved -2m, in the second second, the object moved -2m again and in the third second it moved -2m for a total of 6m over the 3 seconds. confidence assessment: 3
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16:44:37 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 --> I see. The position can be positive or negative, but the total displacement cannot be negative, therefore the velocity cannot be negative. self critique assessment: 2
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16:47:15 `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: 3
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16:47:27 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 --> self critique assessment: 3
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16:48:15 `q007. How do you write the expressions `ds and `dt on your paper?
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RESPONSE --> I write them with a delta, a small triangle shape in place of `d. confidence assessment: 3
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16:48:30 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 --> self critique assessment: 3
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16:51:58 `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 --> The object moves 5m/s * 10s = 50m. In this problem, the average rate of 5m/s specifies how often the position of the object changes. confidence assessment: 3
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16:53:34 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 --> We would divide the rate by the second quantity to arrive at the first. self critique assessment: 3
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16:54:57 `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: 3
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16:55:06 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 --> self critique assessment: 3
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16:57:46 `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 --> vAve, `dt, and `ds are related to the definition of a rate by being the change in a value with respect to another value. In the case of vAve, it is the change in position with respect to time. confidence assessment: 3
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16:58:23 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 --> I could have written out the equation vAve = `ds/`dt. self critique assessment: 2
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17:01:27 `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 --> We multiply both sides of the equation by `dt vAve = `ds / `dt vAve * `dt = `ds / `dt *`dt vAve * `dt = `ds confidence assessment: 3
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17:01:42 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 --> self critique assessment: 3
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17:06:47 `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 --> We intuitively think about multiplying the rate by the clock time to arrive at the displacement. confidence assessment: 3
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17:07:13 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 could have given an example rather than a geralization. self critique assessment: 3
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17:20:29 `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 --> We multiply both sides by `dt, then divide both sides by vAve. vAve = `ds/`dt vAve * `dt = `ds/`dt *`dt vAve * `dt = `ds (vAve * `dt)/vAve = `ds/vAve `dt = `ds/vAve confidence assessment: 3
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17:20:50 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 --> self critique assessment: 3
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17:23:23 `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 --> If we drive at 25 miles at 5mph it will take us 25mi/5mph = 5 hours to get there. confidence assessment: 3
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17:23:35 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 --> self critique assessment: 3
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