Find the times t in the open interval 0

Question

Find the times t in the open interval 0<t<5 at which the particle changes direction. 
v(t)=ln(t^2 - 3t + 3)

darkigloo · Answer

it also says the particle is at position x=8 at t=0 if that matters

anonymous · Answer

Do you have any thoughts already?

darkigloo · Answer

i know that if velocity is positive, the particle is moving left. if velocity is negative, the particle is moving right.

anonymous · Answer

Are you sure?

darkigloo · Answer

o.o i thought so

darkigloo · Answer

oh wait no..

anonymous · Answer

Didn't you make a typo?

darkigloo · Answer

if velocity is negative, it moves left. if velocity is positive it moves right.

anonymous · Answer

It's so good that you finally got it.

darkigloo · Answer

^.^ but i'm sure there's more to the question.

anonymous · Answer

OK. When a particle's direction tends to change?

darkigloo · Answer

i don't know :/

anonymous · Answer

Assuming you are moving straightly to the right. What if you wanted to change your direction toward the left? What would happen to your speed while you're changing your direction?

darkigloo · Answer

it would become 0?

anonymous · Answer

Yes, you now got it. The last step you need to do is to find the zeros of that function.

darkigloo · Answer

so x=1 and x=2. do oi plug in a number between 0 and 1, 1 and 2, and 2 and 5 to see if it is negative/positive?

anonymous · Answer

Yes, so we infer immediately that at the two points the direction of the particle will change. Yes, you can plug in numbers to see the direction. But it is not already asked about the direction. Don't worry about it.

darkigloo · Answer

got it thanks> can you help me with another part of the question?

anonymous · Answer

I am to get going. Hurry up...

darkigloo · Answer

ok sorry :/ 
the average speed of the particle over the interval 0<= t <= 2

anonymous · Answer

It is too much calculations. You have to obtain the position function x(t) from v(t). [ x(t) = int v(t)dt]

Once you get the function x(t) from integration, you'll need to use the average speed function at the interval (0,2). It is defined as
$$\Delta x/ \Delta t = (x_2 - x_1)/(t_2 - t_1)$$
where t_2 - t_1 = 2 - 0 = 2.

You just need to find the respected x values and put them at that function.

darkigloo · Answer

Alright. Thank you.

anonymous · Answer

Take care!

darkigloo · Answer

same to you.