# Thread: position, velocity, and acceleration problem

1. ## position, velocity, and acceleration problem

I am reviewing for AP Calc test and I need some help b/c i don't remember how to quite do this problem.

the position of a particle moving along a straight line is given by
$s=t^3-6t^2+12t-8$
a. the minimum value of the speed is:
(A) 1 (B) 2 (C) 3 (D) 0 (E) none of these

b. the speed of the particle is decreasing for:
(A) t>2 (B) t<3 (C) all t (D) t<1 or t>2 (E) none of these

2. Originally Posted by yoman360
I am reviewing for AP Calc test and I need some help b/c i don't remember how to quite do this problem.

the position of a particle moving along a straight line is given by
$s=t^3-6t^2+12t-8$
a. the minimum value of the speed is:
(A) 1 (B) 2 (C) 3 (D) 0 (E) none of these

b. the speed of the particle is decreasing for:
(A) t>2 (B) t<3 (C) all t (D) t<1 or t>2 (E) none of these
Dear yoman360,

First differentiate the given equation with respect to x and then factorize it. Afterwards by setting $\frac{dy}{dx}=0$ you could find the minimum speed. Also by considering $\frac{dy}{dx}$ in the intervals given in part b you could find the interval at which teh particles speed is decreasing.

3. Originally Posted by yoman360
I am reviewing for AP Calc test and I need some help b/c i don't remember how to quite do this problem.

the position of a particle moving along a straight line is given by
$s=t^3-6t^2+12t-8$
a. the minimum value of the speed is:
(A) 1 (B) 2 (C) 3 (D) 0 (E) none of these

b. the speed of the particle is decreasing for:
(A) t>2 (B) t<3 (C) all t (D) t<1 or t>2 (E) none of these
The velocity is the derivative of the position function. Since the position function is cubic, the velocity is a quadratic function of the time. Completing the square in that quadratic will answer all of these questions.

4. thanks
for
a. I got (D) 0 minimum at t=2 plug 2 into velocity function and got 0
b. i got (E) none of these because the speed is always positive except for t=2 where speed is 0.

CORRECT?

5. Originally Posted by yoman360
thanks
for
a. I got (D) 0 minimum at t=2 plug 2 into velocity function and got 0
b. i got (E) none of these because the speed is always positive except for t=2 where speed is 0.

CORRECT?
Dear yoman360,

Yes you are correct. Hope you have understood the concepts well.

Goodbye!!

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### s=t^3-6t^2 12t-8

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