Expert: Paul Klarreich - 3/13/2011

Question
A particle is moving along a horizontal line according to the equation
      s=t^3-12t^2+36t-24 t>or=0
Determine the intervals of time when the particle is moving to the right and when it is moving to the left. Also determine the instant when the particle reverses its direction.


Pls. explain the answer.

Answer
Questioner: Chakaron
Country: Philippines
Category: Calculus
Private: No
Subject: instantaneous velocity and acceleration
Question: A particle is moving along a horizontal line according to the equation
     s = t^3 - 12t^2 + 36t - 24,  t >= 0
>> You will want to know when  v(t) = s'(t) is positive, negative, or zero.
>> Start by differentiating  s

v = 3t^2 - 24t + 36

v = 3(t^2 - 8t + 12)

Set it = 0 and solve;  you get  t = 2,  t = 6.

Those are your critical points.


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Determine the intervals of time when the particle is moving to the right
>> that means  v is positive.

and when it is moving to the left.
>> v is negative.

Also determine the instant when the particle reverses its direction.

>> that's your  t = 2, t = 6.

Your intervals will be [0,2],  [2,6] and [6,..]

I leave it to you to test whether v is positive or negative in those intervals.