An object moves uphill in a potential

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When an object moves "uphill" in a potential, the work done on it is negative, indicating a decrease in kinetic energy. This means the object will move slower as it ascends to a higher potential. The mathematical representation involves integrating the gradient of potential energy. Understanding this concept is crucial for analyzing energy changes in physical systems. The discussion highlights the relationship between potential energy and kinetic energy during such movements.
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an object moves "uphill" in a potential

=-\int_{1}^{2}\nabla\mbox{U}\cdot\mbox{dr}\

=-\int_{1}^{2}\mbox{dU}

How can this be?

Any help would be appreciated. Thank you
 
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This says, essentially, that if an object moves "uphill" in a potential, the work done on the object is negative and so it will have less kinetic energy (move slower) when it moves towards a higher potential.
 
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