A particle is moving in a straight line. Its displacement, metres, from the origin, , at time seconds, where  , is given by  .

1. Find the initial displacement of the particle.  (1 mark)
   

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2. Find the velocity of the particle as it passes through the origin.  (3 marks)
   

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3. Show that the acceleration of the particle is always negative.  (1 mark)
   

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4. Sketch the graph of the displacement of the particle as a function of time.  (2 marks)
   

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The displacement of a particle moving along the  -axis is given by

 ,

where    is the displacement from the origin in metres,    is the time in seconds, and  .

1. Show that the acceleration of the particle is always negative.    (2 marks)
   

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2. What value does the velocity approach as    increases indefinitely?    (1 mark)
   

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