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Unformatted text preview: 7.87: a) Eliminating in favor of and ) ( x x = , . ) ( 2 2 2 2 2 2 - =- =- = x x x x x x x x x x x x x U ) 1 1 ( ) ( 2 =- = x x U . ) ( x U is positive for x x < and negative for x x ( and must be taken as positive). b) . 2 2 ) ( 2 2 - =- = x x x x mx U m x v The proton moves in the positive x-direction, speeding up until it reaches a maximum speed (see part (c)), and then slows down, although it never stops. The minus sign in the square root in the expression for ) ( x v indicates that the particle will be found only in the region where < U , that is, x x . c) The maximum speed corresponds to the maximum kinetic energy, and hence the minimum potential energy. This minimum occurs when = dx dU , or , 2 3 2 3 =...
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