The slope of kinetic energy displacement curv | vedclass

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Question

(c) $E = \frac{1}{2}m{v^2}.$ Differentiating w.r.t. $x$, we get

$\frac{{dE}}{{dx}} = \frac{1}{2}m 	imes 2v\frac{{dv}}{{dx}} = mv 	imes \frac{{dv}

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Directly proportional to the acceleration

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(c) $E = \frac{1}{2}m{v^2}.$ Differentiating w.r.t. $x$, we get

$\frac{{dE}}{{dx}} = \frac{1}{2}m 	imes 2v\frac{{dv}}{{dx}} = mv 	imes \frac{{dv}}{{dt}} 	imes \frac{{dt}}{{dx}} = mv 	imes \frac{a}{v} = ma$

The slope of kinetic energy displacement curve of a particle in motion is

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