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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?

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4 answers
  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.

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    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.

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  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.

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    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.

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