MHB 2.1.2 AP calculus Exan particle move along the x-axis

[karush]

A particle moves along the x-axis. The velocity of the particle at time t is $6t - t^2$.
What is the total distance traveled by the particle from time $t = 0$ to $t = 3$
ok we are given $v(t)$ so we do not have to derive it from a(t) since the initial $t=0$ we just plug in the $t=3$ into $v(t)$ so
$6(3) - (3)^2=18-9=9$.
I thot I might of posted this earlier but I could not find it

 

[Greg]

Hmmm... $p(t)=3t^2-\frac{t^3}{3}+C$ (Wondering)

 

[karush]

isn't that for a(t) ??

 

[Greg]

$p'(t)=v(t),\quad v'(t)=a(t)$

 

[skeeter]

total distance = $\displaystyle \int_{t_1}^{t_2} |v(t)| \, dt$