Phy 201
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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 automobile moves 10 m in 8 seconds. This gives It an average velocity of 10m/8sec or 1.25m/sec.
The second automobile moves 10m in 5 seconds or 2m/sec. These are average velocities and since the initial velocity is 0m/s, the final velocity is 2x this average. This means the first vehicle has a final velocity of 2.5m/sec and the second has a final velocity of 4m/sec. Acceleration=’dv/’dt so
Acceleration for 1= 2.5m/sec/8sec= .313m/s/s
And acceleration for 2= 4m/sec/5sec= 0.8m/s/s
Now we need to compare these to the slopes. A slope of .05 has an acceleration of .313m/s/s, while a slope of .10 has an acceleration of .8m/s/s. Therefore I would conclude that the acceleration increases with the slope at a rate of ‘da/’ds which would be (.8-.313)/(.1-.05)=9.74
So every increase of 1 in slope would lead to an increase in acceleration of 9.74m/s/s.
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15 mins
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