(Solved): The particle travels along the path defined by the parabola \( y=0.5 x^{2} \), where \( x \) and \ ...

The particle travels along the path defined by the parabola \( y=0.5 x^{2} \), where \( x \) and \( y \) are in \( \mathrm{ft} \). When \( t=0, x=0, y=0 \). (Figure 1) If the component of velocity along the \( x \) axis is \( v_{x}=(2 t) \mathrm{ft} / \mathrm{s} \), where \( t \) is in seconds, determine the particle's distance from the origin \( O \) when \( t=1 \mathrm{~s} \). Express your answer using three significant figures and include the appropriate units. Part B Determine the magnitude of the particle's acceleration when \( t=1 \mathrm{~s} \). Figure Express your answer using three significant figures and include the appropriate units.