Measuring MotionChapter 11

What is Motion?• Motion is changing position along a certain path.• In the first part of physical science, we have 2 goals:

• To understand how things move (kinematics)• To understand why things move (dynamics)

How do things move?• Vocabulary

• Frame of reference• Distance• Displacement• Speed• Velocity• Slope• Acceleration• Gravity

• As we go through the section, create flashcards for these words.

Frame of Reference• A reference point is a starting point… a place that everyone

calls zero.• When everyone knows where 0 is, then it is much easier to

describe the location or position of objects.• Example: In races, the starting line is 0, or your reference

point. Everything is measured from the starting line.

Distance vs. Displacement

• Distance is the total path an object travels. • Measures how far an object

moves along a path.

• Displacement is the line from the beginning to the end.• Measures how far between

the starting point and ending point.

Start

End

Distance vs. Displacement• You start at your house (0). You go to the store. Then you go to your

friend’s house.• What is the distance that you travel?

• 8 houses• What is your displacement from the beginning to the end?

• 2 houses

0 storefriend

Speed vs. Velocity• Speed describes how fast an object is moving.• Velocity is an object’s speed in a particular direction.• Ex. Does your car’s speedometer read speed or velocity?

• Speed• What could make this a velocity?

• If your car also has a compass in it.

Variables

• Time is shown as a little t.• “t” is measured in seconds, usually.

• Sometimes minutes or hours

• Distance is shown as a little d or a little x.• “d” or “x” both mean the same thing.• Usually measured in meters

• Sometimes kilometers, miles, feet, or inches

• Velocity & speed are shown as little v.• “v” is usually measured in m/s

• Sometimes mph, km/hr, ft/s

Finding speed and velocity• To calculate speed, you need to know 2 things

• Distance that an object traveled (in meters)• Time it took to travel that distance (in seconds)

Speed = distance time Or

Units for speed and velocity:m/s or km/hr or miles/hour

Calculating• Examples:

• Find the speed of a runner who runs 120m, south in 2 minutes. d = 120m t = 2 min = 120sv = 120m 120s = 1m/s

• For velocity, we need to specify direction.• 1m/s, SOUTH

• Find the distance a horse travels, who is galloping at 15m/s for 90 seconds.

V = 15 m/s t = 90s

15m/s = d 90sd = 15m/s x 90sd = 1350m

Problems for you

p. 369: practice problems: #1-3

Graphing Motion• To investigate the relationship between distance and time,

you can use• Mathematical equations

or• Graphs of distance vs. time

Dis

tanc

e (m

)

Time (s)

Here is an example of a distance vs. time graph.• What can it tell us?

• Where the object was at any time.

• How long it took the object to travel a certain distance.

• The speed of the object. = SLOPE

What is slope? • In math, to find slope, you

have to • Pick 2 points

• A = (5s, 15m)• B = (15s, 45m)

• Calculate rise• Change in y = rise• 45m -15m = 30m

• Calculate run• Change in x = run• 15s – 5s = 10s

• Slope = rise run• 30m 10s = 3m/s

A

B

Definition: How steep a line is

What does the slope mean?

• The slope of a distance vs. time graph gives us the velocity.

• For the object graphed below, the velocity is 3m/s in the positive direction.

Direction from a graph• Line A is in the positive direction, because x is steadily

increasing as time increases.• Line C is in the negative direction, because x is steadily

decreasing as time increases.• What direction is the object in line B going?

• Positive direction

A

B

C

What else does this graph tell us?

• It tells us • Starting position of each object• Ending position of each object• Speed and direction of each object• Which object is going faster or fastest

A

B

C

What else does this graph tell us?

• What is B’s speed?1.33m/s

• Who is going faster, A or B?A

• How could we tell that without doing the math?because the line of B is not as steep as A’s line

A

B

C

• What does a flat horizontal line mean?• Time

• Increasing

• Distance• Staying the same

• Speed• None. The object is not moving D

ista

nce

(m)

Time (s)