A particle's velocity is $v(t)=3t^2-12t+9$ m/s. At $t=0.5$ seconds, which statement describes the particle's motion?

Core Concept

At $t=0.5$, $v(0.5)=3.75>0$, so the particle moves right. Since $a(t)=6t-12$ gives $a(0.5)=-9<0$, velocity and acceleration have opposite signs and the particle slows down.