# Motions involving Acceleration, Velocity and Time

\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) […]