6 A particle moves with constant speed on a circular path of radius 2 metres. The centre of the circle has position vector \(2 \mathbf { j }\) metres.
At time \(t = 0\), the particle is at the origin and is moving in the positive \(\mathbf { i }\) direction.
The particle returns to the origin every 4 seconds.
The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular.
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1. Calculate the angular speed of the particle.
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2. Write down an expression for the position vector of the particle at time \(t\) seconds.
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3. Find an expression for the acceleration of the particle at time \(t\) seconds.
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4. State the magnitude of the acceleration of the particle.
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5. State the time when the acceleration is first directed towards the origin.