Assgn5

course Phy201

????K????????assignment #005005. Uniformly Accelerated Motion

Physics I

07-08-2008

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21:01:03

`q001. Note that there are 9 questions in this assignment.

If the acceleration of an object is uniform, then the following statements apply:

1. A graph of velocity vs. clock time forms a straight line, either level or increasing at a constant rate or decreasing at a constant rate.

2. The average velocity of the object over any time interval is equal to the average of its velocity at the beginning of the time interval (called its initial velocity) and its velocity at the end of the time interval (called its final velocity).

3. The velocity of the object changes at a constant rate (this third statement being obvious since the rate at which the velocity changes is the acceleration, which is assumed here to be constant).

4. The acceleration of the object at every instant is equal to the average acceleration of the object.

Suppose that an object increases its velocity at a uniform rate, from an initial velocity of 5 m/s to a final velocity of 25 m/s during a time interval of 4 seconds.

By how much does the velocity of the object change?

What is the average acceleration of the object?

What is the average velocity of the object?

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RESPONSE -->

The velocity of the object change 20m/s

The average acceleration of the object is 5m/s^2

The average velocity of the object is 5m/s

confidence assessment: 1

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21:02:41

The velocity of the object changes from 5 meters/second to 25 meters/second so the change in velocity is 20 meters/second. The average acceleration is therefore (20 meters/second) / (4 seconds) = 5 m / s^2. The average velocity of the object is the average of its initial and final velocities, as asserted above, and is therefore equal to (5 meters/second + 25 meters/second) / 2 = 15 meters/second (note that two numbers are averaged by adding them and dividing by 2).

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RESPONSE -->

I got everything correct except the last one.....i had 15m/s....but i thought it was only when acceleration was uniform that you did that, but i understand my error.

self critique assessment: 2

The velocity increases at a uniform rate, which is identical in meaning to the condition of uniform acceleration.

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21:08:48

`q002. How far does the object of the preceding problem travel in the 4 seconds?

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RESPONSE -->

60 meters i believe, if the average velocity is 15m/s and you going to travel 4 seconds....the its 15m/s *4s

confidence assessment: 0

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21:09:27

The displacement `ds of the object is the product vAve `dt of its average velocity and the time interval, so this object travels 15 m/s * 4 s = 60 meters during the 4-second time interval.

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RESPONSE -->

I answered the question correctly

self critique assessment: 3

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21:18:13

`q003. Explain in commonsense terms how we determine the acceleration and distance traveled if we know the initial velocity v0, and final velocity vf and the time interval `dt.

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RESPONSE -->

well vf+v0/2=vAve, then you can take that number and multiply it by the time interval to get you distance traveled. I thought acceleration was constant in that one. Anyhow you can get aAve= 'dv/'dt

confidence assessment: 1

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21:19:01

In commonsense terms, we find the change in velocity since we know the initial and final velocities, and we know the time interval, so we can easily calculate the acceleration. Again since we know initial and final velocities we can easily calculate the average velocity, and since we know the time interval we can now determine the distance traveled.

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RESPONSE -->

I believe I understood that, i just put them in expression form.

self critique assessment: 3

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21:26:03

`q004. Symbolize the situation by first giving the expression for the acceleration in terms of v0, vf and `dt, then by giving the expression for vAve in terms of v0 and vf, and finally by giving the expression for the displacement in terms of v0, vf and `dt.

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RESPONSE -->

acceleration=v0+vf/2*'dt

this is not correct; go back to the definition of acceleration to see why this doesn't work

vAve=vf+v0/2

displacement=v0+vf/2*'dt

This is correct, provided you put parentheses around your numerator; but the right-hand side is identical to what you identified as acceleration in your first statement.

Again, be sure you understand how the definitions of average velocity and average acceleration apply in this situation.

confidence assessment: 1

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21:27:27

The acceleration is equal to the change in velocity divided by the time interval; since the change in velocity is vf - v0 we see that the acceleration is a = ( vf - v0 ) / `dt.

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RESPONSE -->

I missed this one...i believe i had the first two right just not the expression for acceleration.

self critique assessment: 3

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21:29:21

When this average velocity is multiplied by `dt we get the displacement, which is `ds = (v0 + vf) / 2 * `dt.

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RESPONSE -->

I understand this now....i believe i had displacement right anyhow.

self critique assessment: 3

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21:36:03

`q006. This situation is identical to the previous, and the conditions implied by uniformly accelerated motion are repeated here for your review: If the acceleration of an object is uniform, then the following statements apply:

1. A graph of velocity vs. clock time forms a straight line, either level or increasing at a constant rate or decreasing at a constant rate.

2. The average velocity of the object over any time interval is equal to the average of its velocity at the beginning of the time interval (called its initial velocity) and its velocity at the end of the time interval (called its final velocity).

3. The velocity of the object changes at a constant rate (this third statement being obvious since the rate at which the velocity changes is the acceleration, which is assumed here to be constant).

4. The acceleration of the object at every instant is equal to the average acceleration of the object.

Describe a graph of velocity vs. clock time, assuming that the initial velocity occurs at clock time t = 0.

At what clock time is the final velocity then attained?

What are the coordinates of the point on the graph corresponding to the initial velocity (hint: the t coordinate is 0, as specified here; what is the v coordinate at this clock time? i.e., what is the velocity when t = 0?).

What are the coordinates of the point corresponding to the final velocity?

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RESPONSE -->

vf=v0+a*'dt

0,0

I don't have enough information to figural out vf in this problem. The only thing i have is the initial velocity

confidence assessment: 0

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21:38:01

The initial velocity of 5 m/s occurs at t = 0 s so the corresponding graph point is (0 s, 5 m/s). The final velocity of 25 meters/second occurs after a time interval of `dt = 4 seconds; since the time interval began at t = 0 sec it ends at at t = 4 seconds and the corresponding graph point is ( 4 s, 25 m/s).

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RESPONSE -->

I understand the question now, but I didn't understand what numbers I was suppose to use. I didn't know we were suppose to use the initial number from the first one, i didn't write those down.

self critique assessment: 1

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21:39:29

`q007. Is the graph increasing, decreasing or level between the two points, and if increasing or decreasing is the increase or decrease at a constant, increasing or decreasing rate?

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RESPONSE -->

I would say the graph is increasing, and increasing at a constant rate

confidence assessment: 1

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21:41:58

Since the acceleration is uniform, the graph is a straight line. The graph therefore increases at a constant rate from the point (0, 5 m/s) to the point (4 s, 25 m/s).

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RESPONSE -->

I understand the acceleration was uniform and constant, but i do not see how those coordinates form a straight line. I guess i'm not picturing this one in my head exactly right?????

self critique assessment: 2

You need to sketch the graph on paper; visualizing it isn't sufficiently concrete. On a graph of v vs. t the vertical axis measures v and the horizontal axis measures t. Thus for example the point (4 s, 25 m/s) represents the fact that at clock time t = 4 s, the object is moving at 25 m/s.

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21:44:15

`q008. What is the slope of the graph between the two given points, and what is the meaning of this slope?

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RESPONSE -->

slope between these two graph points represents average acceleration for the corresponding time interval

confidence assessment: 1

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21:46:39

The rise of the graph is from 5 m/s to 25 m/s and is therefore 20 meters/second, which represents the change in the velocity of the object. The run of the graph is from 0 seconds to 4 seconds, and is therefore 4 seconds, which represents the time interval during which the velocity changes. The slope of the graph is rise / run = ( 20 m/s ) / (4 s) = 5 m/s^2, which represents the change `dv in the velocity divided by the change `dt in the clock time and therefore represents the acceleration of the object.

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RESPONSE -->

I said the graph represents the average acceleration of the object. I just didn't state that slope=rise/run=20m/s/4s=acceleration=5m/s^2

self critique assessment: 3

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21:53:46

`q009. The graph forms a trapezoid, starting from the point (0,0), rising to the point (0,5 m/s), then sloping upward to (4 s, 25 m/s), then descending to the point (4 s, 0) and returning to the origin (0,0). This trapezoid has two altitudes, 5 m/s on the left and 25 m/s on the right, and a base which represents a width of 4 seconds. What is the average altitude of the trapezoid and what does it represent, and what is the area of the trapezoid and what does it represent?

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RESPONSE -->

The average altitude is the same as the average velocity, which equals 5 m/s. The area of the trapezoid represents the change in position, which equals 20m/s.

confidence assessment: 1

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21:56:50

The two altitudes are 5 meters/second and 25 meters/second, and their average is 15 meters/second. This represents the average velocity of the object on the time interval. The area of the trapezoid is equal to the product of the average altitude and the base, which is 15 m/s * 4 s = 60 meters. This represents the product of the average velocity and the time interval, which is the displacement during the time interval.

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RESPONSE -->

I missed this question entirely, but i do understand; vf+v0/2 =vAve

I didnt' know the formula to figure out base, but i should have figured it out. The vAve*the width or base.

self critique assessment: 2

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Good work. See my notes and let me know if you have questions. &#