(A) Use interval notation to indicate the time interval or union of time
intervals when the particle is moving forward and backward
the particle is
speeding up
<span>if a(t) >0, it means 12t-48>0, and t
>4, I = ]4, infinity[</span>
the particle is
speeding down
<span>if a(t) < 0, it means 12t-48>0, and t <
4, I = ] -infinity, 4[</span>
when the particle is moving forward and backward
that is depending of the sign of v(t)
moving forward if
v(t)> 0
<span>moving backward if
v(t)< 0</span>
but v(t) = 6t² - 48 t
+90, this quadratic equation has exactly two solutions, t =1, and t =3
<span>so after taking care the sign of </span>6t² - 48 t +90,
<span>v(t)> o when t is in I = ] –inf, 1[ U ]4, inf[,the particle
is moving forward</span>
<span>v(t) < o
when t is in I = ]1, 4[,the particle is
moving backward</span>
<span> </span>
