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A typical automobile coasts up a typically paved incline, stops, and coasts back down to the same position.
When it reaches this position, is it moving faster, slower or at the same speed as when it began? Explain
answer/question/discussion: ->->->->->->->->->->->-> :
On the way up, 'dv = - vo = a*'dt, with acceleration being negative and back down the incline.
Since 'dv up = -a*'dt, then under ideal circumstances (no friction) 'dv = a*'dt on the way down, so velocity should be the same, just opposite in direction.
On the way up, vf = 0 m/s, and on the way down vo = 0 m/s, so under ideal conditions, velocity will be the same at a certain point but opposite in magnitude.
With friction however, the car will not attain its ideal PE up the incline, and on its way down it will lose some of its KE converted from PE working on friction, so it will be slower and opposite in direction once it passes the comparison point.
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