Two particles move along a straight line. The first particle, Particle A $,$ travels with a velocity of $\backslash ($ f$($t$)=-2\backslash$sin $(\backslash$pi t$)+3\backslash )$ feet per second. The second particle, Particle B$,$ travels with a velocity of $\backslash ($ g$($t$)=2$ t$-2\backslash )$ feet per second

After $6$ seconds, which particle has traveled farther from their starting point, and how much farther is it ahead?

$($You may enter an exact answer or round to two decimal places$).$

Provide your answer below:

Particle is ahead by feet.