# Velocity

• Mar 6th 2010, 08:33 AM
rawkstar
Velocity
let v(t)=3t^2-12t be the velocity of a particle moving along the x axis for the time t, t>(greater than or equal) 0,
When t=0,the particle is at x=-6

A) determine the position of the particle at t=a
B) write an expression for the speed of the particle at any time t
C) in which direction does the particle begin moving and when does it turn around
D) when, if ever, is the particle at the origin

Ok so i haven't even attemt part A because I don't even know what a means, im guesing you have to integrate it somewhere tho
• Mar 6th 2010, 08:39 AM
Miss
Quote:

Originally Posted by rawkstar
let v(t)=3t^2-12t be the velocity of a particle moving along the x axis for the time t, t>(greater than or equal) 0,
When t=0,the particle is at x=-6

A) determine the position of the particle at t=a
B) write an expression for the speed of the particle at any time t
C) in which direction does the particle begin moving and when does it turn around
D) when, if ever, is the particle at the origin

Ok so i haven't even attemt part A because I don't even know what a means, im guesing you have to integrate it somewhere tho

Right, for (A) , to find the position function ,namely p(t), you should integrate v(t) w.r.t. t :
$\displaystyle p(t)=\int v(t) \, dt = \int (3t^2-12t) \, dt=?$
• Mar 6th 2010, 08:47 AM
rawkstar
p(t)=t^3-6t^2+C
• Mar 6th 2010, 08:51 AM
skeeter
Quote:

Originally Posted by rawkstar
x(t)=t^3-6t^2+C

note that the position function is x(t) (the position x as a function of time)

now use your initial condition ...

Quote:

When t=0,the particle is at x=-6
to find the constant of integration, C.
• Mar 6th 2010, 08:54 AM
rawkstar
ok x(0)=-6
so that means that C=-6
so x(t)=t^3-6t^2-6
• Mar 6th 2010, 09:23 AM
rawkstar
i still have no idea what a is
• Mar 6th 2010, 09:54 AM
skeeter
Quote:

Originally Posted by rawkstar
i still have no idea what a is

Quote:

A) determine the position of the particle at t=a
"a" is just a specific value of t

$\displaystyle x(a) = a^3-6a^2-6$

that's all.
• Mar 6th 2010, 02:18 PM
rawkstar
thank you
i think i got it
for B i just made my speed function f(x)=|3t^2-12t| since speed=|velocity|
for C my answer was left then it changes to right @ 4
for D my answer was approx 6.15