The position of a particle moving horizontally is s$($t$)=2t^3-12t^2+18t+1,$ where s is measured in meters and t is in seconds.

a$.$ Find the velocity and acceleration of the particle as functions of t$.$

b$.$ On what time interval$($s$)$ is the particle moving backwards? Explain your answer.

c$.$ Is the particle speeding up or slowing down at $1\mathrm{.}5$ seconds? Explain your answer