course Phy 201 I feel like it takes me too long to answer these questions and my mind feels too much like a jumbled mess to think for more Q and A.... Mz~QǩEᙫ̅aassignment #001
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16:35:50 What do we mean by velocity?
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RESPONSE --> Velocity shows how fast an object is moving and in what direction. Velocity can also be a negative number and it uses displacment instead of distance traveled.
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16:40:56 How can we determine the velocity of a ball rolling down an incline?
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Determine initial position and final position, subtract the initial from the final position and divide by the time that elapsed. 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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16:44:53 ** 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 --> Notes taken.
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16:51:33 We anticipate from our experience that a ball traveling down a greater incline, starting from rest, will experience a greater change in velocity. 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 --> To determine if there is a change in velocity one must find the average acceleration, which is the change of velocity divided by the time elapsed.
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16:55:03 ** 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 --> notes taken.
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16:57:47 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 --> notes taken.
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17:08:24 ** 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 --> I didn't answer that question because I thought the answer was given...But I took notes of both the short and detailed answer.
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17:15:40 How do we determine the rate at which the velocity changes? How can we understand the concept of the rate at which velocity changes?
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RESPONSE --> To determine the rate at which the velocity changes one must find the average acceleration. Ave. acceleration of an object moving in a straight line is represented by the slope of a graph of velocity vs. clock time. The acceleration function is the derivative of the velocity function for an object.
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17:17:10 ** 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 --> notes taken.
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17:33:19 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 --> Change in velocity is the rise and change in time is the run, which equals the slope. The change in position is the area under a v vs. t graph.
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17:37:08 ** 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 --> Answer understood, notes taken.
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17:41:28 What does the graph of position vs. clock time look like for constant-acceleration motion?
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RESPONSE --> The line is curved upward as position and time increases.
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17:50:37 ** 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 --> I should have went into more detail...Notes taken.
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17:58:10 How can we obtain a graph of velocity vs. clock time from a position vs. clock time graph?
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RESPONSE --> To obtain a velocity vs. clock time graph from a position vs. clock time graph by taking the position, `ds and divide it by the clock time, `dt of the position vs. clock time graph.
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18:09:27 ** 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 --> I did the misconception...but I understand. Notes taken.
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18:15:55 How can we obtain a graph of position vs. clock time from a velocity vs. clock time graph
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RESPONSE --> To find displacement on a velocity vs clock time graph, take the average velocity and multiply by the change in time, `dt.
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18:22:14 ** 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 --> Notes taken. Answer understood.
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18:29:29 How can we obtain a graph of acceleration vs. clock time from a velocity vs. clock time graph?
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RESPONSE --> Find the average of the initial and final velocities of the desired time interval and divide it by the desired time interval.
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18:38:19 ** 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 --> Notes taken.
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18:48:10 How can we obtain a graph of velocity vs. clock time from an acceleration vs. clock time graph
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RESPONSE --> Take the average acceleration (m/s/s) and add it to the velocity at the clock time t = 0, t = 1, t = 2, etc.
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18:51:27 ** 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 --> notes taken.
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