Ask questions and get helpful responses.
Ask a New Question
  1. Questions

Calculus

1. A particle moves along the x-axis in such a way that it's position in time t for t is greater or equal to 0 is given by x= 1/3t^3 - 3t^2 +8t
A. Find the position of the particle at time t = 3.
B. Show that at time t = 0, the particle is moving to the right.
C. Find all values of t for which the particle is moving to the left.
D. What is the total distance the particle travels from t = 0 to t = 4?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Cameron

  1. (A) just plug in t=3
    (B) v(t) = -(9t^2-6t+8)/(3t^3 - 3t^2 +8t)^2 so t(0) < 0
    (C) the denominator is never negative, so where is the numerator negative?
    hint: the discriminant is never zero
    (D) s = ∫[0,4] √(1+(x')^2) dt
    = ∫[0,4] √(1+1/(9t^2-6t+8)^2) dt = 4.01
    though actually, since x(0) = ∞, I'd say the distance traveled must also be infinite.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A particle moves in the xy plane with constant acceleration. At time zero, the particle is at x = 6.0 m, y = 3.0 m, and has velocity v = 4.0 m/s + -1.0 m/s . The acceleration is given by the vector a = 4.0 m/s2 + 0 m/s2 . (a) Find

  2. Calculus

    The velocity of a particle on the x-axis is given by the differential equation dx/ dt= t^2/ 2 and the particle is at x = 4 when t = 2. The position of the particle as a function of time is: A. x(t) = t^3 / 6 - 26/3 B. x(t) =t +2

  3. Calculus - Still Need Help! Anyone!

    A particle moves along the x-axis with position at time t given by x(t)=e^(-t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify

  4. 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

  1. CALCULUS BC

    a particle moves on the x-axis in such a way that its position at time t is given by x(t)=3t^5-25^3+60t. for what values of t is the particle moving to the left. a.-2

  2. Calculus

    A particle moves along the x-axis so that it’s position s in meters at any time t>0 in seconds is given by the function s(t)=2t+2sin((pi/2)t). A. Find the velocity of the particle, and then determine the velocity at times t=1

  3. calculus

    Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t

  4. calculus

    5. A particle moves along the x-axis in such a way that its position at time t is given by x=3t^4-16t^3+24t^2 for -5 ≤ t ≤ 5. a. Determine the velocity and acceleration of the particle at time t. b. At what values of t is the

  1. Physics

    I need help with this question with explanation. Thanks A particle of mass m starts from rest at position x = 0 and time t = 0. It moves along the positive x-axis under the influence of a single force Fx = bt, where b is a

  2. 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

  3. calculus

    Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration. A particle moves along the x-axis at a velocity of v(t) = 5/√t, t > 0. At

  4. calculus

    5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? Why? b. Find the acceleration of the particle at time t= 1.5. Is

Still need help? You can ask a new question.