Ch. 2 - 3

Displacement, Velocity, and Acceleration

Vocabulary Mechanics – the study of the motion of

objects

Kinematics – Describing the motion of objects with words, diagrams, graphs and mathematical equations

Vocabulary Vector – a quantity (thing that can be

measured) which contains both a size (magnitude) and direction. Ex:

Scalar – a quantity which is completely described with a magnitude and has no associated direction Ex:

- Some things are by nature a scalar or a vector, some are DEFINED to be a scalar or a vector

Distance vs. Displacement vs. Position Distance – total path length travelled

Scalar

Displacement – length from starting to ending point. vector Points FROM starting point TO ending point

Position – measured from origin (you set coordinate system!)

Calculating Displacement

Speed vs. Velocity Speed – “How fast” = distance / time

Defined to be a scalar Equation for AVERAGE speed:

Velocity – “how fast and in what direction” = DISPLACEMENT/time Defined as a vector (needs direction!) Equation for AVERAGE velocity:

Calculating Velocity

Acceleration “how quickly something speeds up” AND/OR

“how quickly something changes direction” Equation for average acceleration:

Direction of acceleration (in 1-D)

Ticker-Tape Diagrams (aka particle diagrams) Dot represents the “center of mass” of the

object Like a strobe light picture – equal intervals of

time occur between each recorded dot Examples:

Vector Diagrams (aka motion diagrams) Use a picture of the object (sometimes a dot)

along with vectors to represent the motion of an object

Length of arrow represents size of vector quantity

Examples:

Position vs. Time Graphs Position on y-axis Time on x-axis Example with constant velocity

Slope of line =

Time (s)

Position (m)

0 0

1 3

2 6

3 9

4 12

5 15

Position vs. time graphs - examples

Velocity vs. Time graphs Velocity on y-axis; time on x-axis Example – constant acceleration:

Slope of velocity vs. time graph =

Time (s)

Velocity (m/s)

0 2

1 4

2 6

3 8

4 10

Velocity vs. Time Graph - examples

Velocity vs. Time graph – finding displacement Displacement = AREA between line and x-axis

Area above the x-axis is positive displacement, area below is negative displacement

Example

Equations of Kinematics Velocity with average accel. equation

Equations of Kinematics Displacement as area under position vs. time

graph:

Equations of Kinematics Final velocity squared

Kinematics Example: Dimensional Analysis

Kinematics Example:

Kinematics Example:

Free-FallAn object is in free fall if its motion is only being affected by gravity

- air resistance is not a factor (negligible)- not being propelled by its own power

source- generally assumed to be on earth, unless

otherwise specified- can be going up OR down!

Examples:

Acceleration Due to Gravity Galileo’s Experiment (*demo/video demo)

Acceleration due to gravity (on Earth) =

Free Fall ex: Object is dropped

Free Fall ex: Obj. is thrown upward

Free Fall ex: Obj. is thrown downward