Question

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

Moderate

Solution

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

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