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course phy 121
2:43 2/10
he problem:A ball starts with velocity 0 and accelerates uniformly down a ramp of length 30 cm, covering the distance in 5 seconds.
What is its average velocity?
answer/question/discussion (start in the next line)
V=d/t =30/5= 6
V= vf+vo/2 =6+0 /2= 3
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vAve is (change in position) / (change in clock time.
I don't recommend the formula d / t, which has a number of ambiguities; though if you can use it and avoid the ambiguities it's OK.
However the ambiguity did confuse you here. You apparently have mistaken the v from the formula you used for vf. This is just a case in point illustrating why I do not recommend that formula.
The letter v should never be used in analyzing the motion of an accelerating object. This is because we have
v0, the initial velocity
vf, the final velocity
vAve, the average velocity
`dv, the change in velocity.
The symbol v, or the idea of 'the velocity' could easily be confused with any of these. This is the reason I don't use the symbol or the term in this context.
In other words, there is no such thing in the analysis of motion on an interval as 'the velocity'. There are at least four important quantities that are velocities, and we will avoid errors if we are careful to specify these using the appropriate notation and adjective.
That's a lot of words to tell you that you have calculated the average velocity, not the final velocity, with your v = d / t calculation. You then averaged that with the initial velocity, which clearly won't give you the average velocity.
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If the acceleration of the ball is uniform then its average velocity is equal to the average of its initial and final velocities.
You know its average velocity, and you know the initial velocity is zero.
What therefore must be the final velocity?
answer/question/discussion (start in the next line):
Vf=v0+at
=0 + (3/5) 5
Vf=3 cm/s
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By how much did its velocity therefore change?
answer/question/discussion (start in the next line):
It increased by 3 cm/s
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At what average rate did its velocity change with respect to clock time?
answer/question/discussion (start in the next line):
(3-0)/ (5-0)=3/5 cm/s
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What would a graph of its velocity vs. clock time look like? Give the best description you can.
answer/question/discussion (start in the next line):
The graph would be increasing.
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You are using a formula and a notation that differs from the recommended notation. This has led you to some fundamental errors.
It's easy to understand the likely reason why you used that formula. The formula is unfortunately given in most textbooks, so I suspect you got it out of yours. So I'm not criticizing you for using it, just pointing out in detail why I think the formula is a big mistake on the part of many authors.
Bottom line: that formula has mislead you and I suggest you never use it. Stick with the notation I've introduced, which isn't difficult to learn and which saves a lot of confusion.
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