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Mechanics, EXT2* M1 2019 HSC 13c

A particle moves in a straight line. At time    seconds the particle has a displacement of m, a velocity of    and acceleration  .

Initially the particle has displacement  0 m  and velocity  . The acceleration is given by  . The velocity of the particle is always positive.

  1. Show that  .  (2 marks)

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

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i.   
 
 
   

 

 

 

 

ii.   
 
 
   
   

 

♦ Mean mark part (ii) 46%.

Mechanics, EXT2* M1 2007 HSC 3c

A particle is moving in a straight line with its acceleration as a function of    given by  . It is initially at the origin and is travelling with a velocity of 1 metre per second.

  1. Show that  .  (2 marks)

  2. Hence show that  .  (2 marks)

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i.   

 

 

 

MARKER’S COMMENT: Most candidates “neglected” to consider the two cases that  .

 

 

ii.   

 

 

Mechanics, EXT2* M1 2007 HSC 2d

A skydiver jumps from a hot air balloon which is 2000 metres above the ground. The velocity, metres per second, at which she is falling    seconds after jumping is given by  .

  1. Find her acceleration ten seconds after she jumps. Give your answer correct to one decimal place.  (2 marks)

  2. Find the distance that she has fallen in the first ten seconds. Give your answer correct to the nearest metre.  (2 marks)

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i.     
   
 
   
   

 

 
 
 

 

ii.