Results 1 to 2 of 2

Math Help - differentiation - displacement, speed

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    176

    differentiation - displacement, speed

    bk2 p90 q24 c d
    i don't know how to do c) and d)
    question: The displacement x at time t of a particle is given by
    x = A sin 2t + B cos 2t
    where A and B are constants.
    a) if x satisfies the equation
    \frac {d^2 x }{dt^2} + 3 \frac {dx}{dt} - 4x  = sin 2t
    find the values of A and B
    b) What is the max. displacement of the particle?
    c) show that the speed at time t is given by 2 \sqrt {A^2 +B^2 - x^2}
    d) hence find the maximum speed of the particle

    my working:
    dx/dt = 2A cos 2t - 2B sin 2t
    \frac {d^2 x }{dt^2}  = -4A sin 2t - 4B cos 2t
    A = -2/25
    B = -3/50
    when dx/dt = 0
    tan 2t = 4/3
    sin 2t = 4/5 or -4/5
    cos 2t = 3/5 or -3/5
    max. of x = 1/10
    don't know how to do c) and d) . thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by afeasfaerw23231233 View Post
    bk2 p90 q24 c d
    i don't know how to do c) and d)
    question: The displacement x at time t of a particle is given by
    x = A sin 2t + B cos 2t
    where A and B are constants.
    a) if x satisfies the equation
    \frac {d^2 x }{dt^2} + 3 \frac {dx}{dt} - 4x = sin 2t
    find the values of A and B
    b) What is the max. displacement of the particle?
    c) show that the speed at time t is given by 2 \sqrt {A^2 +B^2 - x^2}
    d) hence find the maximum speed of the particle

    my working:
    dx/dt = 2A cos 2t - 2B sin 2t
    \frac {d^2 x }{dt^2} = -4A sin 2t - 4B cos 2t
    A = -2/25
    B = -3/50
    when dx/dt = 0
    tan 2t = 4/3
    sin 2t = 4/5 or -4/5
    cos 2t = 3/5 or -3/5
    max. of x = 1/10
    don't know how to do c) and d) . thanks
    d) From (c), the speed will be a maximum when x is a minimum. Can you find the minimum value of x .....?

    To get the result in (c):

    v = 2 A \cos (2t) - 2 B \sin (2t) \Rightarrow v^2 = .......... ~ .... (1)

    x = A \sin (2t) + B \cos (2t) \Rightarrow x^2 = .......... \Rightarrow 4 x^2 = ......... ~ .... (2)

    (1) + (2): v^2 + 4x^2 = 4B^2 + 4A^2 \Rightarrow ......
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. displacement
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 28th 2010, 05:33 PM
  2. final speed from escape speed
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: November 21st 2009, 01:23 PM
  3. Differentiation(average speed)
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 3rd 2009, 01:52 AM
  4. angular speed, tangetial speed.
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: November 24th 2007, 10:31 AM
  5. Converting horizontal speed to vertical speed
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: July 27th 2006, 06:23 AM

Search Tags


/mathhelpforum @mathhelpforum