Position velocity acceleration

Lessons

• 1.
  The position of a particle moving along a straight line is given by:
  
  $s(t)=t^3-12t^2+36t-14$
  
  where t is measured in seconds and s in meters.
  a)

  Find the position of the particle at: t=0,1,2,3,4,5,6,7, and draw a diagram to illustrate the positions of the particle.
  
  
  b)

  Find the velocity at time t.
  
  
  c)

  Find the velocity of the particle at: t=1,3,5,7.
  
  
  d)

  When is the particle:
  i) at rest?
  ii) moving forward (that is, moving in the positive direction)?
  iii) moving backward (that is, moving in the negative direction)?
  Draw a diagram to illustrate the motion of the particle.
  
  
  e)

  Find the total distance traveled by the particle during the first 7 seconds.
  
  
  f)

  Find the acceleration at time t.
  
  
  g)

  Compare the velocity and acceleration of the particle at: t=1,3,5,7, and determine whether the particle is speeding up or slowing down at each instant.
  
  
  h)

  Graph the position, velocity, and acceleration functions for
  $0 \leq t \leq 7.$
  
  
  i)

  When is the particle:
  i) speeding up?
  ii) slowing down?
  
  

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