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.
   1. 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.
   2. Find the velocity at time t.
   3. Find the velocity of the particle at: t=1,3,5,7.
   4. 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.
   5. Find the total distance traveled by the particle during the first 7 seconds.
   6. Find the acceleration at time t.
   7. 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.
   8. Graph the position, velocity, and acceleration functions for
      $0 \leq t \leq 7.$
   9. When is the particle:
      i) speeding up?
      ii) slowing down?