representing motion

Chapter 2

What kinds of motion can you describe?How do you know that an object has moved?

Be specific. Let’s start at the very beginning… Straight

Line Motion.

A series of images showing the positions of a moving object at equal time intervals is called a motion diagram.

A particle model is a simplified version of a motion diagram in which the object in motion is replaced by a series of single points.

Coordinate SystemsTells you the location of the zero point of the

variable you are studying and the direction in which the values of the variable increase.

The origin is the point at which both variables have a value of zero

Position can be represented by drawing an arrow from the origin to the point representing the object’s new locationThe length of the arrow indicates how far the

object is from the origin or the distance.

Have magnitude (size) and direction

Require the use of VECTOR ADDITION to determine resultant vector

Only have magnitudeCan be added or

combined using standard rules of addition and subtraction

Scalars

Vector Scalar

Displacement Distance

Velocity Speed

Acceleration Time

Force Temperature

You will need a ruler, protractor, and pencilDraw a coordinate system (small) as your

originDraw an arrow with the tail at the origin and

the head pointing in the direction of motion.The length of the arrow should represent the

distance traveled.Add the second vector using the

head to tail method.Measure resultant magnitude and direction.

Add vectors using “head to tail” method.Pictures do not need to be drawn to scale.

No need for a ruler and protractor.Use Pythagorean Theorem and SOHCAHTOA

to solve for resultant vectors ONLY when RIGHT TRIANGLES are formed.

If not right triangles, use Law of Sines and Law of Cosines to solve for resultant vectors.

222 cba

c

C

b

B

a

A sinsinsin cos2222 abbac

The difference between two times is called a time interval and is expressed as

i and f can be any two time variables you choose (according to each problem)

A change in position is referred to as displacement.

if ttt

if ddd

Distance ≠ DisplacementDisplacement is the shortest distance from start to finish

or “as the crow flies”Draw the following:

10m East -10m10m North + 12m West

Every vector has x- and y- components.In other words, a vector pointing southwest has

both a south (y) and west (x) component.Vectors can be “resolved into c0mponents”.Use SOHCAHTOA to find the x- and y-

components

Break EACH vector into x- and y- components.

Assign negative and positive values to each component according to quadrant rules. For instance, south would have a negative sign.

Add the x- column. Add the y- column.Use Pythagorean Theorem to determine the

final displacement magnitude.Use SOHCAHTOA to find the final

displacement direction.

Plot time on the x-axis and position on the y-axisSlope will indicate average velocityUse this website for extra help.

http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm

Shape of Slope Interpretation

Linear Constant speed(can be positive or negative)

Parabolic Speeding up

Hyperbola Slowing down

Average velocity is defined as the change in position, divided by the time during which the change occurred.

On a position vs. time graph, both magnitude and relative direction of displacement are given. A negative slope indicates an object moving toward the zero position.

if

if

tt

dd

t

dv

Speed simply indicates magnitude or “how fast.”

Velocity indicates BOTH magnitude and direction. In other words velocity tells you “how fast” and “where.”

When solving for average velocity, two points for position and time are chosen for comparison. Individual changes in speed could have taken place within those intervals.

Instantaneous velocity represents the speed and direction of an object at a particular instant.

On a position-time graph, instantaneous velocity can be found by determining the slope of a tangent line on the curve at an given instant.

So far, we have looked at motion diagrams, particle models, and graphs as a means of representing motion.

Equations are also quite useful.Based on the equation y=mx +b, one final

equation will be derived in this chapter.

idtvd d = final positionv = average velocityt = time intervaldi = initial position (based on y-intercept if using a graph)

Read Chapter 1! You will reinforce all of these concepts, drill them into your head and see more examples than I have given here.

Visit www.physicsclassroom.com This website offers great explanations of physics concepts.

Watch this video. It is a little boring but very helpful. http://www.youtube.com/watch?v=4J-mUek-zGw