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Thread starter samuelclarke
Start date May 11, 2012

samuelclarke

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May 11, 2012

How do we prove

a=d(1/2 v^2)/dx given that a point is moving along a number line with velocity V m/s?

$\\ \frac{d}{dx} \left ( \frac{1}{2} v^2 \right ) \\\\ = \frac{1}{2} 2 v \times \frac{dv}{dx} $ by the Chain Rule.$ \\\\ = v \times \frac{dv}{dx} \\\\ = v \times \frac{dv}{dt} \times \frac{dt}{dx} \\\\ = a \times v \times \frac{dt}{dx} $ but remember that $ \frac{dx}{dt} = v \Rightarrow \frac{dt}{dx} = \frac{1}{v} \\\\ = a$

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