# [SOLVED]-2.1.207 AP calculus Exan particle move along the x-axis

#### karush

##### Well-known member
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
$6(3) - (3)^2=18-9=9$.

hopefully
any sugestions?

I thot I might of posted this earlier but I could not find it

#### Greg

##### Perseverance
Staff member
Hmmm... $p(t)=3t^2-\frac{t^3}{3}+C$

#### karush

##### Well-known member
isn't that for a(t) ??

#### Greg

##### Perseverance
Staff member
$p'(t)=v(t),\quad v'(t)=a(t)$

#### skeeter

##### Well-known member
MHB Math Helper
total distance = $\displaystyle \int_{t_1}^{t_2} |v(t)| \, dt$