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# C3 Questions watch

1. 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.
2. 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
3. (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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