The Concepts

In particle motion problems, we have three equations we will work with:

$LaTeX: s(t) \text{ or } x(t) \text{ or } y(t)$ describes the position of the particle, when using we are looking at the particle moving left and right and for we are looking at the particle moving up and down.
describes the velocity of the particle.
describes the acceleration of the particle.

And we can answer questions about...

Particle Motion Question Types
Statement	Translation	Steps to Solve
The particle has stopped...	when (i.e. the velocity of the particle is 0).	Set and solve for .
The particle is moving to the right (or up)...	when (i.e. the velocity of the particle is positive).	Set and solve for using a sign table or the graph of .
The particle is moving to the left (or down)...	when (i.e. the velocity of the particle is negative).	Set and solve for using a sign table or the graph of .
The particle has changed directions or turned around...	when $LaTeX: v(t) \text{ changes signs}$ (i.e. the velocity of the particle changes from + / -)	Check for sign changes on the sign table or crossing the -axis for the graph of .
The particle is speeding up...	when $LaTeX: v(t) \text{ and } a(t) \text{ have the same signs}$ (i.e. when the particle is moving and accelerating in the same direction)	Check signs of $LaTeX: v(t) \text{ and } a(t)$ on sign tables of graphs and see where they have the same sign.
The particle is slowing down...	when $LaTeX: v(t) \text{ and } a(t) \text{ have opposite signs}$ (i.e. when the particle is moving and accelerating in different directions)	Check signs of $LaTeX: v(t) \text{ and } a(t)$ on sign tables of graphs and see where they have opposite signs.

Want notes and examples? Here are the completed notes from class: Particle Motion Notes. You also have my hand-written, color-coded notes.

Check out this great Geogebra visualization for straight line motion which I demo in the video below:

Flipped Math
- 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
TBIL Calculus
- 3.1 Tangents motion, and marginals (AD1)
DeltaMath
- 👩‍🏫 3.1

Here are some skill builders: