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PHY 121
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An automobile rolls 10 meters down a constant incline with slope .05 in 8 seconds, starting from rest. The same automobile requires 5 seconds to roll the same distance down an incline with slope .10, again starting from rest.
At what average rate is the automobile's acceleration changing with respect to the slope of the incline?
answer/question/discussion: ->->->->->->->->->->->-> n:
`ds = 10m
`dt = 8sec
V0 = 0m/s
`ds = (v0 + vf)/2 * `dt
`ds/`dt = (v0+vf)/2
2(`ds/`dt) = v0 + vf
Vf = 2(`ds/`dt) + v0
Vf = 2(10m/8sec) + 0m/s
=2.5m/s
aAve = (2.5m/s - 0m/s)/8sec
=.3125m/s^2
For `dt = 5sec
Vf = 2(10m/5sec) + 0m/s
Vf = 4m/s
aAve = (4m/s - 0m/s)/5sec
=.8m/s^2
(.4875m/s^2)/.05 increase in slope
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Good. You can divide this out. You get about 9.7 m/s^2 / unit of slope.
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&#Good responses. See my notes and let me know if you have questions. &#