course Phy 121 µ£œ„¿ä®Õ©sŸqºŸ´ÆóÌ”ÆõÒ{assignment #001
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14:07:48 `questionNumber 10000 What do we mean by velocity?
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RESPONSE --> Velocity is an average rate that is the change in displacement of an object divided by the change in clock time.
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14:08:03 `questionNumber 10000 ** STUDENT RESPONSE:Velocity is the speed and direction an object is moving. INSTRUCTOR COMMENT: Good. More succinctly and precisely velocity is the rate at which position is changing. obtained by dividing change in position by change in clock time **
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RESPONSE --> okay
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14:08:46 `questionNumber 10000 How can we determine the velocity of a ball rolling down an incline?
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RESPONSE --> To find velocity which is an average rate you find the change in the displacement of the object and divide it by the change in the clock time.
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14:08:59 `questionNumber 10000 ** We divide displacement by the time interval to get average velocity. If the ball happens to be starting from rest and acceleration is uniform we can also conclude that the final velocity attained on the incline is double the average velocity. **
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RESPONSE --> okay
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14:11:25 `questionNumber 10000 We anticipate from our experience that a ball traveling down a greater incline, starting from rest, will experience a greater change in velocity. ÿ How can we determine whether the velocity actually changes, and whether the velocity increases in the manner that we expect?
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RESPONSE --> You can start the clock time when the ball leaves its resting state hit the clock time when it is half way through the distance and then when it finishes going down the incline hit the clock time again. You can then find the velocity for the first half of the distance and then for the 2nd half of the distance and compare the two. The ball rolling down the second half of the incline should have a faster velocity than the first.
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14:11:29 `questionNumber 10000 ** We divide displacement by the time interval to get average velocity. We time the ball down one incline, then down the other and determine average velocity for each. We then infer that since both balls started from rest, the greater average velocity implies a greater change in velocity. **
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RESPONSE --> okay
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14:14:34 `questionNumber 10000 How could we determine the velocity of the ball at a specific point? The specific points are measured for distance and the ball is timed when it reaches these specific points. The distance is then divided by the time.
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RESPONSE --> You just take the displacement from point to point divided by the time interval.
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14:14:49 `questionNumber 10000 ** Short answer: The question concerned one specific point. We can't really measure this precisely. The best we can do is use two points close together near the point we are interested in, but not so close we can't measure the time accurately enough to trust our result. More detailed answer: The question really asks how we determine the velocity at a given point, for an object in the real world. Assuming that the velocity is always changing, how can we ever know the velocity at an instant? This involves a limiting process, thinking of shorter and shorter time intervals and shorter and shorter position changes. If we know the velocity function, or if we can accurately infer the velocity function from our data, then the velocity of a ball at a specific point is obtained by finding the slope of the tangent line of the position vs. clock time graph at that point, which calculus-literate students will recognize as the derivative of the velocity function. **
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RESPONSE --> okay
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14:17:48 `questionNumber 10000 How do we determine the rate at which the velocity changes?ÿ How can we understand the concept of the rate at which velocity changes?
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RESPONSE --> Velocity is an average rate itself. You can determine the rate at which velocity changes by attempting to figuring out velocities from different points to points to estimate the change. The rate that velocity changes can be positive or negative.
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14:17:55 `questionNumber 10000 ** We find the change in velocity then divide by the change in the clock time. Any rate consists of the change in one quantity divided by the change in another. **
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RESPONSE --> okay
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14:21:29 `questionNumber 10000 It is essential to understand what a trapezoid on a v vs. t graph represents. Give the meaning of the rise and run between two points, and the meaning of the area of a trapezoid defined by a v vs. t graph.
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RESPONSE --> The rise and run between two points is defined as a slope of a line between those two points. To find the change of a quantity during a short amount of time you have to find the area under a trapezoid defined by a v vs t graph.
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14:21:42 `questionNumber 10000 ** Since the rise represents the change in velocity and the run represents the change in clock time, slope represents `dv / `dt = vAve, the average velocity over the corresponding time interval. Since the average altitude represents the average velocity and the width of the trapezoid represents the time interval the area of the trapezoid represents vAve * `dt, which is the displacement `ds. **
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RESPONSE --> okay
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14:24:49 `questionNumber 10000 What does the graph of position vs. clock time look like for constant-acceleration motion?
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RESPONSE --> The graph of position vs. clock time looks like a straight line for constant-acceleration motion because clock time is independent and the position of an object is dependent upon the clock time.
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14:26:03 `questionNumber 10000 ** For constant positive acceleration velocity is increasing. The greater the velocity the steeper the position vs. clock time graph. So increasing velocity would be associated with a position vs. clock time graph which is increasing at an increasing rate. The reason velocity is the slope of the position vs. clock time graph is that the rise between two points of the position vs. clock time graph is change in position, `ds, and run is change in clock time, `dt. Slope therefore represents `ds / `dt, which is velocity. Other shapes are possible, depending on whether initial velocity and acceleration are positive, negative or zero. For example if acceleration was negative and initial velocity positive we could have a graph that's increasing at a decreasing rate. Negative initial velocity and positive acceleration could give us a graph that's decreasing at a decreasing rate. **
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RESPONSE --> okay Increasing velocity means that the graph is increasing at an increasing rate. If there is decreasing velocity that means the graph is decreasing at a decreasing rate.
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14:27:03 `questionNumber 10000 How can we obtain a graph of velocity vs. clock time from a position vs. clock time graph?
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RESPONSE --> Take the velocity and multiply it by the clock time in order to get the position. Repeat the process for each desired point.
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14:27:25 `questionNumber 10000 ** We can find the slope of the position vs. clock time graph at a series of clock times, which will give us the velocities at those clock times. We can put this information into a velocity vs. clock time table then plot the velocities vs. clock time as a 'guidepost points', and fill in the connecting curve in such a way as to be consistent with the trend of the slopes of the position vs. clock time graph. COMMON MISCONCEPTION: To get velocity vs. clock time find average velocity, which is position (m) divided by time (s). Plot these points of vAvg on the velocity vs. time graph. INSTRUCTOR RESPONSE: Ave velocity is change in position divided by change in clock time. It is not position divided by time. Position can be measured from any reference point, which would affect a position/time result, but which would not affect change in position/time. Graphically velocity is the slope of the position vs. clock time graph. If it was just position divided by time, it would be the slope of a line from the origin to the graph point. **
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RESPONSE --> okay
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14:28:10 `questionNumber 10000 How can we obtain a graph of position vs. clock time from a velocity vs. clock time graph
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RESPONSE --> For each position divide it by the clock time in order to obtain the velocity and then plot the velocity versus time graph.
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14:28:14 `questionNumber 10000 ** We can divide the graph of v vs. t into small strips, each forming an approximate trapezoid. The area of each strip will represent ave vel * time interval and will therefore represent the change in position during that time interval. Starting from the initial clock time and position on the position vs. clock time graph, we add each subsequent time increment to the clock time and the corresponding position change to the position to get our new position. When the graph is constructed the slopes of the position vs. clock time graph will indicate the corresponding velocities on the v vs. t graph. **
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RESPONSE --> okay
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14:30:21 `questionNumber 10000 How can we obtain a graph of acceleration vs. clock time from a velocity vs. clock time graph?
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RESPONSE --> Acceleration of an object between a two time intervals is the average rate where the velocity changes between the clock times. Plot the points for acceleration on one axis and clock time on the other.
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14:30:37 `questionNumber 10000 ** Accel is the rate of change of velocity, represented by the slope of the v vs. t graph. So we would plot the slope of the v vs. t graph vs. t, in much the same way as we plotted slopes of the position vs. clock time graph to get the v vs. t graph. }University Physics Students note: Acceleration is the derivative of the velocity. COMMON MISCONCEPTION: Take speed/ time to find the acceleration per second. The form an acceleration v. time graph and draw a straight line out from the number calculated for acceleration above. INSTRUCTOR RESPONSE: Ave acceleration is change in velocity divided by change in clock time. (note that this is different from velocity divided by time--we must use changes in velocity and clock time). (Advanced note: Velocity is always measured with respect to some reference frame, and the velocity of the reference frame itself affects a velocity/time result, but which would not affect change in velocity/time). Graphically acceleration is the slope of the velocity vs. clock time graph. If it was velocity divided by time, it would be the slope of a line from the origin to the graph point. **
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RESPONSE --> okay
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14:32:06 `questionNumber 10000 How can we obtain a graph of velocity vs. clock time from an acceleration vs. clock time graph
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RESPONSE --> Average rate where velocity changes is delta velocity per delta clock time which equals average acceleration. You then plot the points for acceleration per clock time.
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14:32:21 `questionNumber 10000 ** STUDENT RESPONSE: Take your acceleration and multiply by time to find the change in velocity. Start with initial velocity and graph your velocity by increasing initial velocity by the slope, or change in velocity. INSTRUCTOR COMMENT: Good. More precisely we can approximate change in velocity during a given time interval by finding the approximate area under the acceleration vs. clock time graph for the interval. We can then add each change in velocity to the existing velocity, constructing the velocity vs. clock time graph interval by interval. A velocity vs. clock time graph has slopes which are equal at every point to the vertical coordinate of the acceleration vs. clock time graph. University Physics students note: These two statements are equivalent, and the reason they are is at the heart of the Fundamental Theorem of Calculus. **
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RESPONSE --> okay"