Your 'cq_1_05.1' 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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The problem:
A ball accelerates at 8 cm/s^2 for 3 seconds, starting with velocity 12 cm/s.
• What will be its velocity after the 3 seconds has elapsed?
a = 8 cm/s^2
t = 3 sec
v 0 = 12 cm/s
v = 12 cm/s + (8 cm/s^2) (3 s)
= 12 cm/s + 24 cm/s
= 36 cm/s
• Assuming that acceleration is constant, what will be its average velocity during this interval?
vAve = (36 cm/s + 12 cm/s) / 2 = 24 cm/s
• How far will it travel during this interval?
`ds = 36 – 12 = 24 cm/s * 3 sec = 72 cm
You get a meaningful result if you divide change in velocity by change in clock time. You do not get a meaningful result if you multiply change in velocity by change in clock time.
'Example: Traveling at a constant 60 mph for 2 hours, the change in velocity is (60 mph - 60 mph) = 0 mph. Multiplying this by `dt = 2 hours we find that we traveled distance (0 mph) * (2 hours) = 0 miles. Obviously we traveled more that 0 miles; this demonstrates that multiplying change in velocity by change in clock time doesn't yield a meaningful result.
vAve = `ds/ `dt so `ds = vAve * `dt, not `dv * `dt.
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Very good, but you fell into a common error on the very last part.
&#Let me know if you have questions. &#