Phy 231
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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.
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At what average rate is the automobile's acceleration changing with respect to the slope of the incline?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
For the first automobile,
vAve = 10 m/8 s = 1.25 m/s
so (0 + vf)/2 = 1.25 m/s
vf = 2.5 m/s
and a = dv/dt = (2.5 m/s - 0 m/s)/8 s = 0.3125 or roughly 0.31 m/s^2
For the second automobile,
vAve = 10 m/5 s = 2 m/s
so (0 + vf)/2 = 2 m/s
vf = 4 m/s
and a = dv/dt = (4m/s - 0 m/s)/5 sec = 0.8 m/s^2
Since the first automobile has .05 slope and 0.31m/s^2, and the second automobile has .10 slope and 0.8m/s^2,
(.8-.31)/(.1 - .05) = 9.8 m/s^2 per unit (1) of slope
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10 min
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&#Very good responses. Let me know if you have questions. &#