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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.
v0 = 10cm/s, vf = 20cm/s
You are given three of the quantities. You have identified two of them correctly.
What is the third?
• 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.
a = 10cm/s^2, vf = 50cm/s, `dt = 3 seconds
• A ball travels 30 cm along an incline, starting from rest, while accelerating at 20 cm/s^2.
`ds = 30cm, a = 20cm/s^2
You are given three of the quantities. You have identified two of them correctly.
What is the third?
Then for each situation answer the following:
• Is it possible from this information to directly determine vAve?
First situation: Yes it is directly determined. vAve = (vf + v0)/2 => (20cm/s + 10cm/s)/2 => 15cm/s
Second situation: no, it can be determined but not directly.
a = (vf-v0)/`dt , therefore, 10cm/s^2 = (50cm/s – v0)/3sec, 30cm/s=50cm/s – v0 => 20cm/s = v0 vAve = (vf + v0)/2 = (50cm/s + 20cm/s)/2 = 70cm/s / 2 = 35cm/s
This is still direct reasoning, employing only the definitions of velocity and acceleration and the uniformity of acceleration and combining the quantities two at a time to build the solution. However it's not as direct as the first.
Third situation: It is not determinable.
This one is determinable, but not directly in the sense that the others were.
If you write the defintions down in terms of v0, vf, `ds, `dt and a you get the first two equations of motion.
This would actually give you two simultaneous equations with unknowns `dt and vf. You could solve those equations simultaneously to find `dt and vf. However this reasoning would not be direct.
The third and fourth equations of motion solve this system of simultaneous equations, one for `ds and the other for vf^2. These equations could be used to solve the third situation.
• Is it possible to directly determine `dv?
First situation: Yes. `dv = vf – v0, `dv = 20cm/s – 10cm/s, `dv = 10cm/s
Second situation: Not directly.
Third situation: No
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20 mins
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