math

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.
x(t) = t3 − 12t2 + 21t − 7, 0 ≤ t ≤ 10
(a) Find the velocity and acceleration of the particle.
x' (t) =

x'' (t) =

  1. 👍 0
  2. 👎 0
  3. 👁 82
  1. Find the open t-intervals on which the particle is moving to the right. (Enter your answer using interval notation.)

    1. 👍 0
    2. 👎 0
  2. moving to the right means x is increasing, so x' > 0
    x = t^3 − 12t^2 + 21t − 7
    x' = 3t^2 - 24t + 21 = 3(t^2-8t+7) = 3(t-1)(t-7)
    x" = 6t - 24 = 6(t-4)
    so, check where x' > 0 (hint: not between the roots, since it is a parabola which opens up)
    Remember the domain.

    1. 👍 0
    2. 👎 0
    posted by oobleck
  3. (0,1)?

    1. 👍 0
    2. 👎 0
  4. no, duh. it is negative between the roots, which are NOT at 0 and 1!

    1. 👍 0
    2. 👎 0
    posted by oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc

    A particle moves along the x-axis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3 - 3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for

    asked by Aparna on January 27, 2013
  2. Calc

    A particle moves along the x-axis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3 - 3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for

    asked by Nicole on January 25, 2013
  3. 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

    asked by Rachel on October 12, 2014
  4. math

    The acceleration of a particle at a time t moving along the x-axis is give by: a(t) = 4e^(2t). At the instant when t=0, the particle is at the point x=2, moving with velocity v(t)=-2. Find the position of the particle at t=1/2 if

    asked by Dave on February 23, 2009
  5. math

    A particle is traveling along a one-dimensional path (such as a number line). The position of the particle is governed by the time function x(t) ƒ­ 3t 4 ƒ{16t3 ƒy18t 2 ƒy 2 , where t is in minutes and 0 „T t „T 5 . Answer

    asked by feysal on March 12, 2011
  6. math

    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. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 Find the open

    asked by Anonymous on January 12, 2019
  7. calculus

    A particle moves on the x-axis so that its velocity at any time t is given by v(t) = sin 2t. At t = 0, the particle is at the origin. a)For 0 ≤ t ≤ π, find all values of t for which the particle is moving to the left. b)Write

    asked by Naseba on April 30, 2012
  8. Calculous

    A particle moves along the c-axis so that at time t its position is given by x(t)=t^2-6^t+9t+11 a)What is the velocity of the particle at t=0 b)During what time intervals is the particle moving to the left? c)What is the total

    asked by Yoona on November 20, 2011
  9. physics

    The velocity-versus-time graph is shown for a particle moving along the x-axis. Its initial position is x0 = 1.8m at t0 =0s. Part A What is the particle's position at t=1.0s? Part B What is the particle's acceleration at t= 1.0s?

    asked by anonymous on February 7, 2015
  10. Calculus-particle motion

    1. A particle is moving on the x-axis (or any number line) Its position x(t), or distance from the origin, at the time t is given by x(t)=4t^3-16t^2+15t. t is greater than or equal to 0 a.) Where is the particle when it is at

    asked by Matt on February 7, 2011
  11. Calculus

    The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? b: What is the average velocity of the

    asked by Raul on March 4, 2013

More Similar Questions