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

karush

Well-known member
Jan 31, 2012
2,678
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:rolleyes:
 

Greg

Perseverance
Staff member
Feb 5, 2013
1,382
Hmmm... $p(t)=3t^2-\frac{t^3}{3}+C$ (Wondering)
 

karush

Well-known member
Jan 31, 2012
2,678
isn't that for a(t) ??
 

Greg

Perseverance
Staff member
Feb 5, 2013
1,382
$p'(t)=v(t),\quad v'(t)=a(t)$
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655
total distance = $\displaystyle \int_{t_1}^{t_2} |v(t)| \, dt$