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    Hey,
    Could anyone work the following out please, it was on todays C3 paper (CEA) btw.

    5,
    A particle moves about a fixed pont O so that its displacement, x, from O can be modelled by the equation
    x = t - sin2t
    where t is the time after leaving O and 0«t«π
    Find the maximum displacement of the particle from O.
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    dx/dt = 1 - 2cos2t

    at SPs dx/dt = 0

    so 1 = 2cos2t

    cos2t = 1/2

    2t = π/3, 5π/3

    t = π/6, 5π/6

    If you plot a graph for x against t you see that the graph falls then rises, or you could find d2 x/dt2 to find which is a maximum

    Since it's only between t = 0 and t = π, the point at t = 5π/6 is the maximum so this is the max displacement:

    x = 5π/6 - sin(5π/3)
    = 5π/6 + root3/2
    = 3.48 (3sf)

    Think this is right but I've been wrong a lot lately so you might want a second opinion
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    (Original post by Master Gee)
    dx/dt = 1 - 2cos2t

    at SPs dx/dt = 0

    so 1 = 2cos2t

    cos2t = 1/2

    2t = π/3, 5π/3

    t = π/6, 5π/6

    If you plot a graph for x against t you see that the graph falls then rises, or you could find d2 x/dt2 to find which is a maximum

    Since it's only between t = 0 and t = π, the point at t = 5π/6 is the maximum so this is the max displacement:

    x = 5π/6 - sin(5π/3)
    = 5π/6 + root3/2
    = 3.48 (3sf)

    Think this is right but I've been wrong a lot lately so you might want a second opinion
    yer you're right
    well, i got the same as you (no point writing out working but its the same as yours)
 
 
 
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Updated: June 13, 2005
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