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: ->->->->->->->->->->->-> :
The first ramp has an average velocity of 10m/8sec which is 1.25 m/s. The final velocity is then 2.5 m/s because I just multiply the average velocity by 2. To get the acceleration, I take 2.5 m/s and divide it by 8 seconds which is then 2.5m/s/8sec = 0.313 m/s^2. The second ramp has the same exact solution path. 10m/5sec = 2 m/s. From there the final velocity is 4 m/s. The acceleration is then 4 m/s/ 5 sec = 0.8 m/s^2. Now, since I found the information, I can find the average rate of the automobiles acceleration changing with respect to the slope of the incline. The change in acceleration is 0.8 m/s/s - 0.313 m/s/s = 0.487 m/s/s and then the change in the ramp is 0.10 – 0.05 = 0.05. 0.487 m/s/s / 0.05 is 9.74 m/s/s which is the average rate that I am looking for.
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15 mins
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&#Very good work. Let me know if you have questions. &#