A particle is initially at rest at the origin. Its acceleration as a function of time, , is given by

1. Show that the velocity of the particle is given by  .  (2 marks)
   

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2. Sketch the graph of the velocity for    AND determine the time at which the particle first comes to rest after  .  (3 marks)
   

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3. Find the distance travelled by the particle between    and the time at which the particle first comes to rest after  .  (2 marks)
   

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The acceleration of a particle is given by

,

where    is the displacement in metres and    is the time in seconds. 

Initially the particle is at the origin with a velocity of  .

1. Show that the velocity of the particle is given by
   

    

     .    (2 marks)
   

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2. Find the time when the particle first comes to rest.    (2 marks)
   

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3. Find the displacement,  ,  of the particle in terms of  .    (2 marks)
   

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