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Mechanics, EXT2 M1 2023 SPEC1 8

A body moves in a straight line so that when its displacement from a fixed origin is metres, its acceleration, , is . The body accelerates from rest and its velocity, , is equal to as it passes through the origin. The body then comes to rest again.

Find in terms of for this interval.  (4 marks)

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Mechanics, EXT2 M1 2015 SPEC1 6

The acceleration ms¯² of a body moving in a straight line in terms of the velocity ms¯¹ is given by 

Given that    when  , where is the displacement of the body in metres, find the velocity of the body when    (4 marks)

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COMMENT: Strong log and exponential calculation ability required here.

Mechanics, EXT2* M1 2004 HSC 5a

A particle is moving along the -axis, starting from a position    metres to the right of the origin (that is,    when  ) with an initial velocity of    and an acceleration given by

.

  1. Show that  .  (2 marks)

  2. Hence find an expression for    in terms of  .  (3 marks)

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ii.   
 
 
   

 

 

Mechanics, EXT2* M1 2006 HSC 4c

A particle is moving so that  

Initially    and the velocity, , is  

  1. Show that    (2 marks)

  2. Hence, or otherwise, show that 
     
           (2 marks)

  3. It can be shown that for some constant  ,
     
                (Do NOT prove this.)
     
    Using this equation and the initial conditions, find    as a function of    (2 marks)

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Mechanics, EXT2* M1 2015 HSC 14b

A particle is moving horizontally. Initially the particle is at the origin moving with velocity .

The acceleration of the particle is given by  , where is its displacement at time  .

  1. Show that the velocity of the particle is given by  .  (3 marks)

  2. Find an expression for as a function of .  (2 marks)

  3. Find the limiting position of the particle.  (1 mark)

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ii.  
 
 
   

 

♦ Mean mark 49%.

 

♦ Mean mark 42%.
iii.