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# Maths C3 help watch

1. 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.
2. by 'C3', do you mean... 'M2'?
3. No it's definately C3. We were told to expect questions based on mechanics situations. I do CCEA. It's a heure
4. (Original post by Pheylan)
by 'C3', do you mean... 'M2'?
I think that is still c3 isn't it.
5. 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

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.
6. (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
7. I hope you're not doing AQA! 0.0
8. 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
9. 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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