Problem 11.010 - Particle motion: velocity and position from acceleration
The acceleration of a particle is defined by the relation \( a=3 e^{-0.2 t} \), where \( a \) and \( t \) are expressed in \( \mathrm{ft} / \mathrm{s}^{2} \) and seconds, respectively. Knowing that \( x=0 \) and \( v=0 \) at \( t=0 \), determine the velocity and position of the particle when \( t=0.5 \mathrm{~s} \).
The velocity and position of the particle when \( t=0.5 \mathrm{~s} \) is \( \square \) \( \mathrm{ft} / \mathrm{s} \) and \( \square \) ft, respectively.