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Phy 121
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** CQ_1_07.2_labelMessages **
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: ->->->->->->->->->->->-> scussion:
'ds=10m
'dt=8s
slope=.05
a='ds/(.5*'dt^2)
a=10m/(.5*(8s)^2)
a=10m/32s^2
a=.3125m/s^2
'ds=10m
'dt=5s
slope=.10
a='ds/(.5*'dt^2)
a=10m/(.5*(5s)^2)
a=10m/25s^2
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You have an arithmetic error here; you lost track of that .5 in the denominator.
The correct result will be .8 m/s^2.
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a=.400m/s^2
.400m/s^2-.3125m/s^2=.0875m/s^2
Therefore acceleration is changing .0875m/s^2 with respect to the slope of the incline.
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This would be the change in the acceleration, not the rate of change of acceleration with respect to ramp slope. The requested rate also considers the change in ramp slope.
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