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Phy 121
Your 'cq_1_06.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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For each situation state which of the five quantities v0, vf, `ds, `dt and a are given, and give the value of each.
• A ball accelerates uniformly from 10 cm/s to 20 cm/s while traveling 45 cm.
answer/question/discussion: ->->->->->->->->->->->-> :
Given
v0 = 10cm/s
vf = 20cm/s
‘ds = 45cm
vAve = (v0 + vf) / 2
vAve = ‘ds / ‘dt
‘dt = ‘ds / (v0 + vf) / 2
‘dt = 45cm / (10cm/s + 20cm/s) / 2
‘dt = 45cm / 15cm/s
‘dt = 4s
a = ‘dv / ‘dt
a = (vf - v0) / ‘dt
a = (20cm/s - 10cm/s) / 4s
a = 10cm/s / 4s
a = 2.5cm/s^2
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• A ball accelerates uniformly at 10 cm/s^2 for 3 seconds, and at the end of this interval is moving at 50 cm/s.
answer/question/discussion: ->->->->->->->->->->->-> :
Given
a = 10cm/s^2
‘dt = 3s
vf = 50cm/s
a = (vf - v0) / ‘dt
10cm/s^2 = (50cm/s - v0) / 3s
30cm/s = 50cm/s - v0
v0 = 20cm/s
vAve = (vf + v0) / 2
vAve = ‘ds / ‘dt
‘ds / ‘dt = (vf + v0) / 2
‘ds / 3s = (50cm/s + 20cm/s) / 2
‘ds / 3s = 70cm/s / 2
‘ds / 3s = 35cm/s
‘ds = 105cm
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• A ball travels 30 cm along an incline, starting from rest, while accelerating at 20 cm/s^2.
answer/question/discussion: ->->->->->->->->->->->-> :
Given
‘ds = 30cm
v0 = 0 cm/s
a = 20cm/s^2
vAve = ‘ds / ‘dt
vAve = (vf + v0) / 2
a = (vf - v0) / ‘dt
(vf + v0) / 2 = ‘ds / ‘dt
‘dt = (vf - v0) / a
(vf + v0) / 2 = ‘ds / (vf - v0)/a
(vf + v0) = 2*‘ds*a / (vf-v0)
(vf + v0)(vf-v0) = 2*‘ds*a
vf^2 -vf v0 + vf v0 - v0^2 = 2*‘ds*a
vf^2 = 2*‘ds*a + v0^2
vf = sqrt(2*‘ds*a + v0^2)
vf = sqrt(2*30cm*20cm/s^2 + (0cm/s)^2)
vf = sqrt (1200cm^2/s^2) + 0cm/s
vf = 34.64cm/s
a = (vf - v0) / ‘dt
20cm/s^2 = (34.64cm/s - 0cm/s) / ‘dt
20cm/s^2 = 34.64cm/s / ‘dt
‘dt = 1.732s
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Then for each situation answer the following:
• Is it possible from this information to directly determine vAve?
answer/question/discussion: ->->->->->->->->->->->-> :
For the first two questions, yes, you are able to directly determine vAve. For the third question, you are not able to directly determine vAve.
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• Is it possible to directly determine `dv?
answer/question/discussion: ->->->->->->->->->->->-> :
For the first two questions, yes, you are able to directly determine ‘dv. For the third question, you are not able to directly determine ‘dv.
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30 minutes
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10/13/11 9:15pm
&#Very good responses. Let me know if you have questions. &#