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 particle on the interval [0,2]?Indicate units of measure
c: Find a formula for the instantaneous velocity of the particle.
d: When is the particle at rest?
e: When is the particle moving to the right? When is it moving to the left?
f: At t=2 seconds, is the particle moving away from the origin or towards the origin?
h: What is the average acceleration of the particle on the interval [0,2]?
i: Find a formula for the instantaneous acceleration of the particle.
j: At t=2 seconds, is the particle slowing down or speeding up?

  1. 👍
  2. 👎
  3. 👁
  1. a) sub in t = 0
    b) avg vel = (s(2) - s(0) )/(2-0) = ...
    c) s ' (t) = 6t^2 - 30t + 24

    d) particle is at rest, when velocity = 0 , that is ...
    6t^2 - 30t + 24 = 0
    t^2 - 5t +4 = 0
    (t-1)(t-4) = 0
    when t = 1 or when t = 4

    f) sub t=2 into the derivative of c)
    if it is positive, ---> to the right
    if it is negative, ---> to the left

    e) same steps as b) except use the velocity expression

    you do some of them.

    1. 👍
    2. 👎
  2. How do you do E on this problem??

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    The velocity graph of a particle moving along the x-axis is shown. The particle has zero velocity at t=0.00s and reaches a maximum velocity, vmax, after a total elapsed time, t total. If the initial position of the particle is x0

  2. AP Calculus

    A particle is moving along a horizontal straight line. The graph of the position function (the distance to the right of a fixed point as a function of time) is shown below. Answer the following questions only on the interval

  3. physics

    The position of a particle moving along the x axis is given by x=3.0t^2 - 1.0t^3 , where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction

  4. physics

    The position of a particle moving along an x axis is given by x = 15t2 - 2.0t3, where x is in meters and t is in seconds. (a) Determine the position, velocity, and acceleration of the particle at t = 3.0 s. x = m v = m/s a = m/s2

  1. calculus

    the position of a particle moving along a coordinate line is s=√(1+4t) , with s in metres and t in seconds. Find the particle's velocity and acceleration at t=6 sec

  2. 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?

  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

  4. 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

  1. Calculus

    The position of a particle moving along the x-axis at time t > 0 seconds is given by the function x(t) = e ^ t - 2t feet. a) Find the average velocity of the particel over the interval [1,3]. b) In what direction and how fast is

  2. physics

    1-The position of a particle moving along the x axis is given by x=t^2-〖2t〗^3-6, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?

  3. Calculus

    A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t)=(t)In(2t). Find the acceleration of the particle when the velocity is first zero. a)2e^2 b)2e c)e d)None of these Any help is greatly

  4. Calc 1

    Consider the position function s(t)=sin((pi)(t)) representing the position of an object moving along a line on the end of a spring. Sketch a graph of s with the secant line passing through (0,s(0)) and (0.5,s(0.5)). Determine the

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