# Position velocity acceleration

##### Examples
###### 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?