$$ \begin{align} a &= \displaystyle \frac{d}{dx} \left( \frac{1}{2} v^2 \right) \\ v &= \frac{dx}{dt} \end{align} $$ Example A particle is moving so that the acceleration \( a = 32x^3 + 48 x^2 + 16x \). Initially \( x=1 \) and \( v=-8 \). Part 1 Show that \( \displaystyle a = \frac{d}{dx} \left( \frac{1}{2}v^2 \right) […]