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.
• At what average rate is the automobile's acceleration changing with respect to the slope of the incline?
answer/question/discussion: ->->->->->->->->->->->-> :
Using the formula for small slopes that acceleration is equal to gravity times the slope: The first acceleration for a slope of .05 the value is .491m/s^2. The second value of acceleration for a slope of .10 is equal to 9.81*.1 which equals .981m/s^2. The average rate that acceleration is changing with respect to slope is equal to .981-.491/(.1-.05) which equals 9.8m/s^3. This number represents the acceleration of gravity per second.
The numerator has units m/s^2; the denominator is unitless. So the units of the slope are m/s^2, and the slope should in fact be equal to the acceleration of gravity.
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5 min.
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