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    I have my C3 exam tomorrow and was going through past papers when I realised I have no idea how to do questions like this;

    A particle travels in a straight line in such a way that its distance x metres from a fixed point O at time t seconds can be given by the equation
    x = 4 + √3 sin 2t + cos 2t
    (ii) Find the rate of change of the distance of the particle from O at time t. [3]
    (iii) Hence find the first time when the particle is at its greatest distance from O. [7]

    I know you have to differentiate to get the velocity, then max displacement occurs when v = 0 but when I looked at the mark scheme I couldn't follow the steps at all, so help would be muchly appreciated.
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    by 'C3', do you mean... 'M2'?
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    No it's definately C3. We were told to expect questions based on mechanics situations. I do CCEA. It's a heure
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    (Original post by Pheylan)
    by 'C3', do you mean... 'M2'?
    I think that is still c3 isn't it.
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    The velocity is 2√3 cos 2t - 2 sin 2t so if you make that equal 0, you'll have:
    2√3 cos 2t - 2 sin 2t = 0
    2√3 cos 2t = 2 sin 2t
    \dfrac{2 \sin 2t}{2 \cos 2t} = \sqrt 3
    \tan 2t = \sqrt 3
    Which you can then solve by doing a quick sketch graph, and finding inverse tan of root 3.

    However, if your exam is tomorrow, you really should be getting some sleep now.
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    (Original post by ebyrne288)
    I have my C3 exam tomorrow and was going through past papers when I realised I have no idea how to do questions like this;

    A particle travels in a straight line in such a way that its distance x metres from a fixed point O at time t seconds can be given by the equation
    x = 4 + √3 sin 2t + cos 2t
    (ii) Find the rate of change of the distance of the particle from O at time t. [3]
    (iii) Hence find the first time when the particle is at its greatest distance from O. [7]

    I know you have to differentiate to get the velocity, then max displacement occurs when v = 0 but when I looked at the mark scheme I couldn't follow the steps at all, so help would be muchly appreciated.
    Hints:
    for ii) rate of change of distance, is just speed, so differentiate distance with respect to t to get speed.

    for iii) i think when the distance is greatest acceleration is 0. so differentiate velocity to get acceleration, as it is the rate of change of velocity, then set a = 0, and solve for t.

    I think, i'm not sitting the exam its been a while
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    I hope you're not doing AQA! 0.0
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    It's tomorrow afternoon and to be honest I don't need much sleep

    Thanks for your help though. There's another one which is exactly the same as the second part of that question but I don't have the mark scheme for that's worth 11 marks. That seems to be too simple to be worth 11 marks. Here's hoping it doesn't come up
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    I've got C3 on ccea tomorrow as well *snap*

    You've got the right idea. Differentiate the expression, set dx/dt = 0 and solve the equation to find t.

    When you differentiate it you get dx/dt = 2√3 cos2t - 2sin2t I think.
 
 
 
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