Welcome, I’m Professor Bob and I’m here to present today’s topic, Graphical Analysis of motion Welcome, I’m Professor Bob and I’m here to present today’s topic, Created by Richard J. Terwilliger August 1998

We are constantly exposed to information in graphical form. Graphical Analysis of motion We are constantly exposed to information in graphical form. Created by Richard J. Terwilliger August 1998

TV all use graphs to display Graphical Analysis of motion Newspapers, magazines, TV all use graphs to display information clearly.

We will look at three different methods of obtaining Graphical Analysis of motion We will look at three different methods of obtaining information from a graph. Created by Richard J. Terwilliger August 1998

the horizontal and vertical axis The first is information off the horizontal and vertical axis Reading Directly Created by Richard J. Terwilliger August 1998

We will refer to information obtained from the horizontal and vertical Vertical (y) Axis Horizontal (x) Axis We will refer to information obtained from the horizontal and vertical axis as a Direct Reading

off the graph. No calculations are involved. Direct Reading This information you Read Directly off the graph. No calculations are involved.

Direct Reading Let’s look at some examples.

Rainfall for Suffern, NY Direct Reading What month had the least amount of rainfall? Inches of Rain 1 2 Month July August September Rainfall for Suffern, NY

Rainfall for Suffern, NY Direct Reading What month had the least amount of rainfall? Inches of Rain 1 2 Month July August September Rainfall for Suffern, NY

Rainfall for Suffern, NY Direct Reading How much rain fell in September? Inches of Rain 1 2 Month July August September Rainfall for Suffern, NY

Rainfall for Suffern, NY Direct Reading What month received 1.75 inches of rain? Inches of Rain 1 2 Month July August September Rainfall for Suffern, NY

Rainfall for Suffern, NY Direct Reading The answers to all of these questions are Inches of Rain 1 2 Month July August September Rainfall for Suffern, NY Direct Readings

from either the horizontal or vertical axis. Direct Reading The answers are read Directly from either the horizontal or vertical axis. Inches of Rain 1 2 Month July August September Rainfall for Suffern, NY Inches of Rain Month

applies to linear motion Direct Reading Let’s look at how a applies to linear motion graphs. Direct Reading

This first graph has TIME on the horizontal axis Direct Reading This first graph has TIME on the horizontal axis DISTANCE (m) 2 4 6 8 and DISTANCE on the vertical axis TIME (s) 1 2 3 4

DISTANCE vs. TIME This is called a DISTANCE vs. TIME graph Direct Reading This is called a DISTANCE vs. TIME graph DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

represents the distance an object travels as it moves along the floor. Direct Reading The purple line represents the distance an object travels as it moves along the floor. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

DISTANCE vs. TIME At what time was the object 6 meters from Direct Reading At what time was the object 6 meters from its starting point? DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

DISTANCE axis, go horizontally over to the purple line and Direct Reading Start at 6 meters on the DISTANCE axis, go horizontally over to the purple line and then drop down to the TIME-axis. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

We read the answer, DISTANCE vs. TIME off the TIME AXIS DISTANCE (m) Direct Reading We read the answer, DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 DIRECTLY off the TIME AXIS TIME (s) 1 2 3 4

DISTANCE vs. TIME How far did the object travel in 2 seconds? Direct Reading How far did the object travel in 2 seconds? DISTANCE vs. TIME 2 4 6 8 DISTANCE (m) TIME (s) 1 2 3 4

go vertically upward to the purple line and then over to the Direct Reading Start at 2 seconds on the TIME AXIS, go vertically upward to the purple line and then over to the DISTANCE AXIS. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

DISTANCE or VERTICAL AXIS Direct Reading The answer is found on the DISTANCE or VERTICAL AXIS DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

C B A Sometimes there are several objects plotted on the same Direct Reading Sometimes there are several objects plotted on the same graph. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 C B A TIME (s) 1 2 3 4

C B A Again, we can ask several questions where the answers are Direct Reading Again, we can ask several questions where the answers are read off the horizontal and vertical axis Directly DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 C B A TIME (s) 1 2 3 4

C B A DISTANCE vs. TIME At what time was object A three meters Direct Reading DISTANCE vs. TIME At what time was object A three meters from its starting point? DISTANCE (m) 2 4 6 8 C B A TIME (s) 1 2 3 4

which object had traveled Direct Reading DISTANCE vs. TIME At a time of one second which object had traveled the greatest distance? DISTANCE (m) 2 4 6 8 C B A TIME (s) 1 2 3 4

B A Here is another graph. SPEED (m/s) TIME (s) Direct Reading 2 4 6 8 1 2 3 4

B A When given a graph, the first thing you should look at Direct Reading When given a graph, the first thing you should look at is what is given on the horizontal and vertical axis. SPEED (m/s) 2 4 6 8 B A TIME (s) 1 2 3 4

for two different joggers. Direct Reading This graph is a SPEED vs. TIME graph for two different joggers. SPEED vs. TIME SPEED (m/s) 2 4 6 8 B A TIME (s) 1 2 3 4

B A Which jogger was traveling the fastest? SPEED vs. TIME SPEED (m/s) Direct Reading Which jogger was traveling the fastest? SPEED vs. TIME SPEED (m/s) 2 4 6 8 B A TIME (s) 1 2 3 4

B A According to the graph, jogger A was traveling at 2 m/s Direct Reading According to the graph, jogger A was traveling at 2 m/s SPEED vs. TIME SPEED (m/s) 2 4 6 8 and jogger B was traveling at 5 m/s. B A TIME (s) 1 2 3 4

B A The answer was SPEED vs. TIME off the vertical axis. SPEED (m/s) Direct Reading The answer was off the vertical axis. SPEED vs. TIME Read Directly SPEED (m/s) 2 4 6 8 B A TIME (s) 1 2 3 4

The second thing we can get Slope The second thing we can get from a graph is it’s DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

Slope The DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

For this graph: DISTANCE vs. TIME DISTANCE (m) TIME (s) Slope 2 4 6 8 1 2 3 4

Created by Richard J. Terwilliger August 1998 Slope and since TIME (s) 1 2 3 4 DISTANCE (m) 6 8 DISTANCE vs. TIME then, the slope of a Distance-Time graph represents the SPEED of the object. Slope = SPEED Created by Richard J. Terwilliger August 1998

We can also use the UNITS to determine what the slope represents. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

DISTANCE vs. TIME DISTANCE (m) TIME (s) Slope Slope = SPEED 2 4 6 8 1 3 4

The SLOPE of a straight line is constant, therefore since the slope of a distance-time graph represents speed, the SPEED shown here is constant. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 SLOPE is CONSTANT TIME (s) 1 2 3 4

The SLOPE of a straight line is constant, therefore since the slope of a distance-time graph represents speed, the SPEED shown here is constant. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 SPEED is CONSTANT TIME (s) 1 2 3 4

Here the SLOPE is increasing, so the SPEED is increasing. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

Here the SLOPE is decreasing, so the SPEED is also decreasing. DISTANCE vs. TIME DISTANCE (m) 2 4 6 8 TIME (s) 1 2 3 4

This graph looks identical to the first distance-time graph Slope This graph looks identical to the first distance-time graph we displayed but now VELOCITY is plotted on the vertical axis 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

This is a VELOCITY vs. TIME VELOCITY vs. TIME graph VELOCITY (m/s) Slope This is a VELOCITY vs. TIME graph VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

Slope Here: VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

Slope Or: VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

Slope VELOCITY vs. TIME 2 4 6 8 8 VELOCITY (m/s) TIME (s) 1 2 3 4

SLOPE of a VELOCITY-TIME Therefore, the SLOPE of a VELOCITY-TIME graph represents ACCELERATION VELOCITY vs. TIME 2 4 6 8 SLOPE = ACCELERATION VELOCITY (m/s) TIME (s) 1 2 3 4

Let’s look at the DISTANCE-TIME graph and VELOCITY-TIME graph Slope Let’s look at the DISTANCE-TIME graph and VELOCITY-TIME graph side-by-side.

DISTANCE vs. TIME VELOCITY vs. TIME DISTANCE (m) VELOCITY (m/s) Slope TIME (s) 1 2 3 4 DISTANCE (m) DISTANCE vs. TIME Slope = SPEED 6 8 TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME Slope = ACCELERATION 6 8

The third method for obtaining information from a graph is AREA The third method for obtaining information from a graph is by determining the VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

under the plotted line. VELOCITY vs. TIME VELOCITY (m/s) TIME (s) AREA 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

Let’s use UNITS to determine AREA Let’s use UNITS to determine what the represents. AREA VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

VELOCITY vs. TIME The 2 is just a number and doesn’t have any AREA AREA VELOCITY vs. TIME The 2 is just a number and doesn’t have any associated units. 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

Therefore: VELOCITY vs. TIME = (s) (m) = (m) (s) VELOCITY (m/s) AREA Therefore: AREA VELOCITY vs. TIME = (s) (m) (s) = (m) 2 4 6 8 VELOCITY (m/s) TIME (s) 1 2 3 4

then the area of a Velocity-Time graph represents either distance If the units for then the area of a Velocity-Time graph represents either distance or displacement. AREA are (meters) VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) AREA DISPLACEMENT is TIME (s) 1 2 3 4

What distance did the object travel during the first three seconds? AREA What distance did the object travel during the first three seconds? VELOCITY vs. TIME 2 4 6 8 VELOCITY (m/s) AREA DISPLACEMENT is TIME (s) 1 2 3 4

To answer this we need to find the area from VELOCITY vs. TIME zero to three seconds. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME 6 8

VELOCITY vs. TIME VELOCITY (m/s) TIME (s) AREA AREA AREA AREA AREA 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME AREA 2 4 6 8 AREA AREA

seconds, the object travels AREA So, from zero to three seconds, the object travels nine meters. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8 AREA

Let’s try another question. AREA Let’s try another question. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME How far did the object travel during the third second? 2 4 6 8

from two to three seconds. AREA Here we need to find the AREA from two to three seconds. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8

We can solve for the area using the equation for a trapezoid or by breaking the area down into a triangle and a rectangle. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8

Lets break the area down into a triangle and a rectangle. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8

VELOCITY vs. TIME (1s)(2m) (1s)(4m) s s VELOCITY (m/s) 2 1m 1m 4m 4m AREA AREA Total AREA AREA TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME AREA Total 2 4 6 8 (1s)(2m) s 2 (1s)(4m) s AREA Total 1m AREA Total 1m 4m 4m 5m AREA Total

According to our calculations of AREA, the object traveled 5 meters during the third second of travel. TIME (s) 1 2 3 4 VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8 1m 4m

Before trying several problems, let’s review what we’ve covered up to this point.

What are the three different methods of obtaining information from a graph? Direct Reading Information read directly off the horizontal and vertical axis. Slope The vertical axis units divided by the horizontal axis units. AREA The vertical axis units times the horizontal axis units.

The following questions will refer to this velocity-time graph which represents the velocity of a car over a period of twenty seconds. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

For every question, you should determine if the question is asking for a Direct Reading TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

For every question, you should determine if the question is asking for a Slope TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

For every question, you should determine if the question is asking for Area TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

This is a direct reading. The answer is read directly off the vertical What is the speed of the car at a time of 2 seconds? This is a direct reading. The answer is read directly off the vertical axis. v2 = 5 m/s TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the car traveling with a constant speed? This is also a direct reading. We need to determine when the velocity is not changing. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

The velocity is constant 4 to 10 seconds When is the car traveling with a constant speed? The velocity is constant 4 to 10 seconds and 14 to 16 seconds. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

This is another direct reading. Between 0 and 4 seconds is the car speeding up or slowing down? This is another direct reading. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

First look at the velocity at 0 seconds. Between 0 and 4 seconds is the car speeding up or slowing down? First look at the velocity at 0 seconds. Then the velocity at 4 seconds. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

Between 0 and 4 seconds is the car speeding up or slowing down? The velocity changed from 0 to 10 m/s therefore the car was speeding up. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

Another direct reading. When does the car have a velocity of +5 m/s? Another direct reading. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

Determine the times when the purple line crosses the +5 m/s line. When does the car have a velocity of +5 m/s? Determine the times when the purple line crosses the +5 m/s line. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

The car has a velocity of +5 m/s at a time of 2 s and 11.3 s. When does the car have a velocity of +5 m/s? The car has a velocity of +5 m/s at a time of 2 s and 11.3 s. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the car slowing down? Here we need to find when the SPEED of the car is decreasing. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the car slowing down? The first section starts at 10 seconds. The car slows down from 10 m/s to 0 m/s. 10 to 12.3 s and … TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the car slowing down? The second section starts at 16 seconds. The car slows down from 5 m/s to 0 m/s. 10 to 12.3 s and 16 to 20 s TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the car slowing down? Remember, velocity is a vector. It is a combination of SPEED and direction. The - sign just shows the direction the car is traveling. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the car accelerating? On a velocity-time graph represents acceleration. SLOPE Therefore, the car is accelerating where the slope is not zero, from 0 - 4 s, 10 - 14 s and 16 - 20 s. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When is the acceleration positive? Here we are looking for a positive SLOPE The slope is positive 0 to 4 s and 16 to 20 s. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When does the car have the greatest acceleration? Here we are looking for the steepest SLOPE TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When does the car have the greatest acceleration? Acceleration is also a vector. Positive and negative slopes only indicate direction, not magnitude. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

When does the car have the greatest acceleration? Therefore the acceleration is the greatest where the slope is the greatest irregardless of the direction. 10 - 14 s TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the acceleration of the car between 10 and 14 seconds? Here we need to determine the between 10 and 14 seconds. SLOPE TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the acceleration of the car between 10 and 14 seconds? To determine the slope at a point, it is necessary to use two points and determine the slope of the line that goes through the point in question. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the acceleration of the car between 10 and 14 seconds? SLOPE = What is the acceleration of the car between 10 and 14 seconds? ACCELERATION = The acceleration for the entire time period of 10 to 14 seconds is -3.75 m/s2. ACCELERATION = TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the acceleration of the car at 12.7 seconds? We know the acceleration between 10 s and 14 s. is -3.75 m/s2 so even though the car is stopped at a time of 12.7 s, it is still accelerating at a - 3.75 m/s2. ACCELERATION = TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

How far does the car travel during the first four seconds? To obtain distance or displacement from a velocity-time graph we need to find: AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

How far does the car travel during the first four seconds? So, we need to solve for the for the first 4 seconds? AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

How far does the car travel during the first four seconds? AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

This time we need to solve for the of a rectangle. How far does the car travel during the time interval of 4 to 10 seconds? This time we need to solve for the of a rectangle. AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

How far does the car travel during the time interval of 4 to 10 seconds? AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

How far does the car travel during the time interval of 10 to 12 How far does the car travel during the time interval of 10 to 12.7 seconds? AREA Again, find the TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

How far does the car travel during the time interval of 10 to 12 How far does the car travel during the time interval of 10 to 12.7 seconds? AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

We need to find the area from 0 to 12.7 seconds. What is the car’s displacement after 12.7 seconds of travel? We need to find the area from 0 to 12.7 seconds. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the car’s displacement after 12.7 seconds of travel? AREA DISPLACEMENT AREA DISPLACEMENT TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the car’s displacement after 12.7 seconds of travel? AREA DISPLACEMENT AREA DISPLACEMENT TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the car’s displacement for the last 7.3 seconds of travel? Again we need to solve for area but this time let’s use the equation for a trapezoid: TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the car’s displacement for the last 7.3 seconds of travel? Equation for a trapezoid: AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

What is the car’s displacement for the last 7.3 seconds of travel? AREA TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

We are looking for the total distance. How far did the car travel from zero to 20 seconds (distance)? We are looking for the total distance. = |93.5 m| + |-23.5 m| = 116.75 m DISTANCE TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

Distance is a scalar quantity so direction isn’t included. How far did the car travel from zero to 20 seconds? Distance is a scalar quantity so direction isn’t included. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

At a time of 20 seconds, how far is the car from its starting point (displacement)? This question is asking for displacement, therefore direction is important. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

At a time of 20 seconds, how far is the car from its starting point? The car went 93.5 meters in the positive direction then 23.25 meters in the negative direction. TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

At a time of 20 seconds, how far is the car from its starting point? = 93.5 m + (-23.25 m) = +70.25 m DISPLACEMENT TIME (s) VELOCITY (m/s) VELOCITY vs. TIME -5 -10 4 8 12 16 20 +10 +5

We worked mainly with two different graphs; a REVIEW We worked mainly with two different graphs; a TIME (s) VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8 1 3 Distance-Time graph and a Velocity-Time graph TIME (s) DISTANCE (m) DISTANCE vs. TIME 2 4 6 8 1 3

A direct reading on the gives us distance and time. REVIEW A direct reading on the gives us distance and time. Distance-Time graph VELOCITY vs. TIME 2 4 6 8 1 3 VELOCITY (m/s) DISTANCE vs. TIME 2 4 6 8 1 3 TIME (s) DISTANCE (m) TIME (s)

A direct reading on the gives us velocity and time. REVIEW A direct reading on the gives us velocity and time. Velocity-Time graph VELOCITY vs. TIME 2 4 6 8 1 3 VELOCITY (m/s) DISTANCE vs. TIME 2 4 6 8 1 3 TIME (s) DISTANCE (m) TIME (s)

The SLOPE of a is graph REVIEW Distance-Time SPEED Slope = SPEED VELOCITY vs. TIME 2 4 6 8 1 3 SPEED VELOCITY (m/s) DISTANCE vs. TIME 2 4 6 8 1 3 TIME (s) DISTANCE (m) Slope = SPEED TIME (s)

The SLOPE of a is graph REVIEW Velocity-Time Slope = ACCELERATION VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8 1 3 ACCELERATION Slope = ACCELERATION DISTANCE vs. TIME 2 4 6 8 1 3 DISTANCE (m) Slope = SPEED TIME (s)

The AREA of a gives us graph REVIEW Velocity-Time Slope = ACCELERATION VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8 1 3 Slope = ACCELERATION DISPLACEMENT DISTANCE vs. TIME 2 4 6 8 1 3 DISPLACEMENT DISTANCE (m) Slope = SPEED TIME (s)

We are not limited to these two graphs so: REVIEW We are not limited to these two graphs so: TIME (s) VELOCITY (m/s) VELOCITY vs. TIME 2 4 6 8 1 3 Slope = ACCELERATION DISTANCE vs. TIME 2 4 6 8 1 3 DISPLACEMENT DISTANCE (m) Slope = SPEED TIME (s)

information from a graph? Whenever you are given a graph remember the three different methods of obtaining information from a graph? Direct Reading Information read directly off the horizontal and vertical axis. Slope The vertical axis units divided by the horizontal axis units. AREA The vertical axis units times the horizontal axis units.

GRAPHICAL ANALYSIS by Richard J. Terwilliger Suffern High School