# Thread: Velocity

1. ## 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

2. 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 :
$p(t)=\int v(t) \, dt = \int (3t^2-12t) \, dt=?$

3. p(t)=t^3-6t^2+C

4. 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 ...

When t=0,the particle is at x=-6
to find the constant of integration, C.

5. ok x(0)=-6
so that means that C=-6
so x(t)=t^3-6t^2-6

6. i still have no idea what a is

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

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

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

that's all.

8. 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

,

### postion of a particle is moving particule turns around at

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