# Position velocity acceleration

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##### Examples

###### Lessons

- 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.- 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.
- Find the velocity at time t.
- Find the velocity of the particle at: t=1,3,5,7.
- 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. - Find the total distance traveled by the particle during the first 7 seconds.
- Find the acceleration at time t.
- 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.
- Graph the position, velocity, and acceleration functions for

$0 \leq t \leq 7.$ - When is the particle:

i) speeding up?

ii) slowing down?