Calculus

The Question: A particle moves along the X-axis so that at time t > or equal to 0 its position is given by x(t) = cos(√t). What is the velocity of the particle at the first instance the particle is at the origin?

So far I was able to determine that the velocity of the particle would be undefined but, I don't understand what it means in the context of this problem for velocity to be undefined. What is the particle doing if its velocity is undefined?

  1. 👍
  2. 👎
  3. 👁
  1. x=cos(sqrt(t))
    v=-sin(sqrt(t))*1/2sqrtt

    wo when is position zero?
    0=cos(sqrt(t))
    sqrt(t)=PI/2
    t=PI^2/4

    v(PI^2/4)=-sin(PI/2)*1/2sqrtPI/2)

    but sin(PI/2)=1
    v(PI^2/4)=1/sqrt(PI/2)= 0.797884561

    So I dont see where the undefined comes from.

    1. 👍
    2. 👎
    👤
    bobpursley
  2. I believe your equation for velocity is incorrect.

    In this case
    V=-sin(sqrt(t))*1/2(sqrt(t))^-1/2

    Your equation for velocity is missing raising to the -1/2 power at the end. applying that piece will make velocity undefined at t=0.

    1. 👍
    2. 👎
  3. Nope.

    x= cos(t^1/2)
    v=-sin(t^1/2) *1/2*1/t^1/2
    = -sin(sqrtt)*1/(2sqrtt) which is what I have. Now, how does having
    sqrt(PI/2) in the denominator make it undefined. I must not be seeing your point.

    1. 👍
    2. 👎
    👤
    bobpursley
  4. Oh lol, I think I see what we're doing differently.

    I thought that the first instance that the particle would be at the origin was when t=0 but it really is when t=pi/2.

    Basically, I substituted the wrong number.

    Thank you, and I'm sorry for not seeing your point.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. PHYSICS

    A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5-s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this

  3. 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

  4. 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

  1. Physics

    Uniform Circular Motion: Suppose that a particle's position is given by the following expression: r(t) = Rcos(omega*t)i + Rsin(omega*t)j 1. Choose the answer that best completes the following sentence: The particle's motion at t=0

  2. Calculus

    1) 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. 2) The driver of a car traveling at 50 ft/sec suddenly

  3. Calculus

    A particle moves along the x-axis with the velocity given by v(t)=3t/(1+t^2) for t >or equal to 0. When t=0, the particle is at the point (4,0). 1. Determine the maximum velocity for the particle. Justify your answer. 2. Determine

  4. Calculus

    At time t >or= to 0, the position of a particle moving along the x-axis is given by x(t)= (t^3/3)+2t+2. For what value of t in the interval [0,3] will the instantaneous velocity of the particle equal the average velocity of the

  1. 12th grade

    A particle starts at x=0 and moves along the x-axis with velocity v(t)=2t+1 for time t is less than or equal to 0. Where is the particle at t=4?

  2. ap calculus

    a particle moves along the x axis in such a way that its acceleration at time t, t>0 , is given by x(t)= (ln x)^2. at what value of t does the velocity of the particle attain its maximum

  3. physic

    The position function x(t) of a particle moving along an x axis is x = 6.00 - 8.00t2, with x in meters and t in seconds. (a) At what time and (b) where does the particle (momentarily) stop? At what (c) negative time and (d)

  4. calculus

    At t=0 , a particle starts at the origin with a velocity of 6 feet per second and moves along the x-axis in such a way that at time t its acceleration is 12t^2 feet per second per second. Through how many feet does the particle

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