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course PHY 241
920pm 11/3/2011
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?
v_0 = 0 cm/s
a = 27 cm/s^2
'ds = 11 cm
`ds = v0 `dt + .5 a `dt^2
since v_0 = 0 cm/s
'ds = 0.5 * a * 'dt^2
(2 * 'ds) / a = 'dt^2
'dt = sqrt[(2 * 'ds) / a]
= sqrt[(2 * 11 cm) / 27 cm/s^2]
= 0.9027 s
The ball spends approximately 0.9 seconds on the first incline
`ds = v0 `dt + .5 a `dt^2
'dt = sqrt[(2 * 'ds) / a]
= sqrt[(2 * 44 cm) / 9 cm/s^2]
= 3.127 s
The ball spends approximately 3.1 seconds on the second incline
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Self-critique (if necessary):
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@& v0 on the second incline is not zero.
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