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course Phy 201
10/5 7There is a question about the units of seconds that I did not understand.
Rand Prob w5q1v1
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course Phy 201
10/ 2
A ball starting from rest rolls 11 cm down an incline on which its acceleration is 27 cm/s2, then onto a second incline 44 cm long on which its acceleration is 9 cm/s2. How much time does it spend on each incline?'ds=v0&'dt+.5a*'dt
11cm=(0)'dt+.5(27cm/s^2)'dt^2
.815s^2='dt^2
.903s='dt
44cm=(0)'dt+.5(9cm/s^2)'dt^2
9.78s='dt^2
3.12s='dt"" &&&&
????????????I'm confused because when you divide cm/cm/s^2=cm*s^2/cm and the cm cancel out leaving only the s^2 and then you take the sqrt of s^2 equals
s???? Or am I doing that wrong?????
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To divide by a fraction you invert it and multiply.
cm / (cm/s^2) = cm * s^2 / cm = (cm / cm) * s^2 = s^2.
The square root of s^2 is s.
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Your method is valid but you need more attention to detail:
If you divide cm by cm/s^2 you don't get units of seconds.
If `dt^2 = 9.78 s, then `dt is about 3.1 s^(1/2).
s^(1/2) is not a unit of time so this couldn't be `dt.
9.13 is very obviously not the square root of 9.78.
And the initial velocity on that second ramp is, in any case, not zero.
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