Calculus

A particle moves on a vertical line so that its coordinate at time t is
3
y = t − 12t+ 3, t≥ 0 .

When is the particle moving upward and when is it moving downward?
Find the distance that the particle travels in the first 3 seconds.

I got that t=2 and t=-2

and its moving upward at (-infitinty,-2) and (-2,2)
and downward and (2, positive infinity)

am I right? If so, how do i find the distance in the first 3 seconds?

  1. 👍 0
  2. 👎 0
  3. 👁 1,416
  1. I'll assume you meant
    y = t^3 - 12t + 3

    the particle is moving downward when y is decreasing; that means y' < 0

    y' = 3y^2-12
    y' < 0 when 3y^2 < 12, or |y| < 2
    So, since t>=0, y is decreasing when 0 <= y < 2.
    upward when y > 2
    So, you are right there, if you remember that t>=0.

    The distance traveled in the first 3 seconds is the difference between where it ended and where it started: y(3)-y(0)
    y(3) = -6
    y(0) = 3

    So, it moved down 9 units in the 1st 3 seconds.

    1. 👍 0
    2. 👎 0
  2. do you mean the other way around, when 0<y<2 it is upward, and downward at y>2

    When I graph it on a number line (how I was taught) that's what I got, but of course I could be wrong.

    1. 👍 0
    2. 👎 0
  3. You are indeed wrong. Here is the graph of y:

    http://www.wolframalpha.com/input/?i=t^3+-+12t+%2B+3

    You can see that y is decreasing for t between 0 and 2.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant.

  2. AP CALC. AB

    A particle moves along a line so that at time t, where 0

  3. Calculus

    A particle moves along a line so that at any time t its position is given by x(t)=2(pi)t+cos(2(pi)t). Determine the particle's maximum velocity.

  4. Calculus

    a particle starts at time t = 0 and moves along the x axis so that its position at any time t>= 0 is given by x(t) = ((t-1)^3)(2t-3) a.find the velocity of the particle at any time t>= 0 b. for what values of t is the velocity of

  1. uniten

    3. At t = 0 , a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with constant accelaration of ( 2.0i - 4.0j ) m/s2 . At the instant the x coordinate of the particle is 15

  2. AP CALC. AB

    1.The position of a particle moving on the line y = 2 is given by x(t)= 2t^3-13t^2+22t-5 where t is time in seconds. When is the particle at rest? a. t =0.268, 2.500, and 3.732 b. t = 0, 1.153, and 3.180 c. t = 1.153, 2.167 and

  3. help math

    a partial moves along the x-axis so that its velocity at time t, for 0< = t = < 6, is given by a differentiable function v whose graph is shown above. The velocity is 0 at t=0, t=5, and the graph has horizontal tangents at t=4.

  4. calculus

    A Particle moves along the x-axis so that at any time t>0, its acceleration is given by a(t)= ln(1+2^t). If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is? The correct answer is

  1. Physics

    A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the v-axis scale is set by vs = 7.0 m/s. (a) What is the

  2. physics

    three point particles are fixed in place in an xy plane. Particle A has mass mA = 3 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other three

  3. Physics

    A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.80 s, it is at point (4.40 m, 6.20 m) with velocity (3.70 m/s) and acceleration in the positive x direction. At time

  4. physics

    Two dimensions. In the figure, three point particles are fixed in place in an xy plane. Particle A has mass mA = 4 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be

You can view more similar questions or ask a new question.