Unit 2 Speed and Graphing

General Physics

Unit 2 – Speed and Graphing

Vocabulary

Section 1.3 Speed (pages 17-21)

Equation

Gives you . . .

If you know . . .

v = d/t

Speed

Distance and time

d = v x t

Distance

Speed and time

t = d/v

Time

Distance and speed

Speed & Velocity Examples

1. If you start from the Art Gallery and travel to the Cafe and back to the Art Gallery in 7200 seconds:

1. What is the distance you travel?

1. What is your displacement?

1. What is your average speed?

1. What is your average velocity?

1. If you start from the Art Gallery and travel to the Cafe in 3600 seconds:

1. What is the distance you travel?

1. What is your displacement?

1. What is your average speed?

1. What is your average velocity?

1. If you start from the Bakery, travel to the Cafe, and then to the Art Gallery in 120 seconds,

1. What is the magnitude of your displacement?

1. What distance did you travel?

1. What is your average speed?

1. What is your average velocity?

1. Sketch your own example of a situation where a person/object travels with the same average speed and average velocity.

1. Sketch your own example of a situation where a person/object travels in two different directions and has a different displacement and distance.

Acceleration Examples

1. A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration?

1. A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many seconds will it take the car to reach a final speed of 25.0 m/s?

1. While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.)

1. A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster?

1. A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at -4.0 m/s2?

1. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this helicopter?

Class Work

1. What is the average speed of a cheetah that sprints 100 m East in 4 s?

What is the cheetah’s average velocity?

1. A runner makes one lap around a 400 m track in a time of 25.0 s. What was the runner's average speed?

What is the runner’s average velocity?

1. A soccer field is about 120 m long. If it takes Alex 10 seconds to run its length, what is his average speed?

1. Calculate the average velocity of a car that drives 50 meters North East in 25 seconds.

1. How long would it take you to run across the high school parking lot if the lot is 50 meters long and you run with an average speed of 5 m/sec?

1. Bart ran 5000 meters from the cops and an average velocity of 6 meters/second West before he got caught. How long did he run?

Group Work

1. What is the average speed of a cheetah that travels 112.0 meters South in 4.0 seconds? What is the cheetah’s average velocity?

1. Samantha runs a 400 m lap in 53.5 s. What is her average speed? What is her average velocity?

1. What is the average speed of a car that traveled 300.0 meters North West in 3600 seconds? What is the cars average velocity?

1. Elmer Fudd shoots a bullet from his rifle with an average speed of 720.0 m/s. What time is required to strike a target 324.0 m away?

Homework

1. On a baseball diamond, the distance from home plate to the pitcher’s mound is 18.5 m. If a pitcher is capable of throwing a ball with an average speed of 38.5 m/s, how much time does it take a thrown ball to reach home plate?

1. A bullet travels with an average velocity of 850 m/s. How long will it take a bullet to go 1000 m?

1. Every summer Mr. Magoo drives to Michigan. It is 3900 m to get there. If he drives with an average speed 100 m/s, how much time will he spend driving?

1. What is the average speed of a cheetah that travels 112.0 meters South in 4.0 seconds? What is the cheetah’s average velocity?

1. After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner’s acceleration?

Challenge Problems

1. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this week. She must get from one side of the school to the other by hurrying down three different hallways. She runs down the first hallway, a distance of 35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and she covers its 48.0 m length at an average speed of 1.20 m/s. The final hallway is empty, and Suzette sprints its 60.0 m length at a speed of 5.00 m/s. Does Suzette make it to class on time or does she get detention for being late again? Show all of your work.

1. During an Apollo moon landing, reflecting panels were placed on the moon. This allowed earth-based astronomers to shoot laser beams at the moon's surface to determine its distance. The reflected laser beam was observed 2.52 s after the laser pulse was sent. The speed of light is 3.0  108 m/s. What was the distance between the astronomers and the moon?

1. For many years, the posted highway speed limit was 88.5 km/hr (55 mi/hr) but in recent years some rural stretches of highway have increased their speed limit to 104.6 km/hr (65 mi/hr). In Maine, the distance from Portland to Bangor is 215 km. How much time can be saved in making this trip at the new speed limit?

1. The tortoise and the hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000. m distance at a speed of 0.2000 m/s while the rabbit runs the first 200.0 m at 2.000 m/s The rabbit then stops to take a nap for 1.300 hr and awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the race and by how much time?

1. Two physics professors challenge each other to a 100. m race across the football field. The loser will grade the winner's physics labs for one month. Dr. Rice runs the race in 10.40 s. Dr. De La Paz runs the first 25.0 m with an average speed of 10.0 m/s, the next 50.0 m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of 11.1 m/s. Who gets stuck grading physics labs for the next month?

Activity – Toy Car

General Physics

Research Question

• What is the relationship between position and time for a moving object?
• What does the slope of a position vs. time graph represent?
• How can we determine if an object moves with constant speed?

Constant speed: The same amount of distance is covered each second.

Hypothesis

As time increases the distance a toy car travels will (increase, decrease, remain the same).

Procedure

1. Choose a starting point for your car. Mark this point with masking tape, and label it “starting point.”

1. Start the car, and place it on the starting point. Release the car (your lab partner should start the stopwatch at the same time). Let the car move in a straight line for 2.0 s. Repeat for several trials, until you find the point that the car consistently crosses after 2.0 s. Mark this point with masking tape, and label it “0.00 m.” Throughout this experiment, you will start the car at the original starting point, but you will begin to measure the distance and time of the car’s motion when the car crosses the 0.00 m mark.

1. Start the car, and place it on the floor at the starting point. Observe the car as it moves. Be sure to start the stopwatch as the car crosses the 0.00 m mark.

1. After 10.0 s, mark the position of the car with the masking tape. Label this mark “10.0 s.”

1. Repeat steps 3 and 4 for 9.0 s, 8.0 s, 7.0 s, 6.0 s, 5.0 s, 4.0 s, 3.0 s, and 2.0 s. Be sure to label each point according to how much time it took for the car to get to that point from the 0.00 m mark.

1. Use the meter stick to measure the exact position from the 0.00 m mark to each time position mark. (Do not measure the distance from the starting point.)

1. For each position marked with tape record in Table 1 on the next page

1 | Page

Research Question

The research questions of this activity was to ______

______

______

______

Hypothesis

I predicted as time increases the distance a toy car travels will (increase, decrease, remain the same) because

______

______

______

Data

Table 1: Position vs. Time

Conclusion

Directions: Answer the following questions in complete sentences.

1) What was the shape of the line on your graph, curved or straight?

______

______

2) Does the shape of your line agree with your hypothesis?

______

______

______

______

3) Did your vehicle move at a constant speed? How do you know?

______

______

______

______

4) What variable did you plot on the y-axis on your graph?

5) What variable did you plot on the x-axis on your graph?

6) Slope refers to the steepness of a line or surface and is found by dividing the change in your vertical axis (rise) over the change in your horizontal axis (run).

The slope of your graph is equal to: answer to #4/answer to #5

Answer to #4 

Answer to #5 

Graphing Little Dudes

General Physics

Suppose something is moving. If you collect corresponding clock reading and position measurements, these numbers form ordered pairs that can easily be graphed. Consider the various little dudes shown below. They exist and move along a sidewalk marked in 1 meter increments. We are given snapshots 2-second time intervals.

1. Draw the line of the graph and label the line, “Walking Dude.”

1. What is the independent variable on the graph?

1. What is the dependent variable on the graph?

1. What does the notation Δ t mean and what is Δ t between 4s and 6s?

1. What does the notation Δ x mean and what is Δ x on the graph between 4s and 6s?

1. What relation can you use to find the slope of the graph, in terms of rise and run?

1. What quantity represents rise on our graph? What represents run?

1. What equation would you use to determine the slope of a position vs. clock reading graph? (Do not use any numbers yet, simply state the equation.) Does this equation look familiar? If not, it is wrong; if so, where have you seen it before?

1. Apply the equation and determine the slope of Walking Dude’s position vs. clock reading graph.

1. On the axes on the front, plot position vs. clock reading for the two other little dudes shown below. Running Dudette starts at 0m and 0s. Reading Dude starts at 8m and 0s. Don’t forget to label.

Running Dudette

Reading Dude

Qualitative graphs

Walk This Way

Purpose

To develop an understanding of motion graphs by analyzing graphs made by walking in front of a motion probe. You will use a motion probe to see what the graph of your motion looks like when you move with increasing, decreasing and constant speed. To collect motion data using an ultrasonic motion detector and analyze plots for evidence that verifies the rules of kinematics.

Research Question

______

Hypothesis

Describe how you would walk to produce a graph of constant speed.

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______

Describe how you would walk to produce a graph of increasing speed.

______

______

Describe how you would walk to produce a graph of decreasing speed.

______

______

Introduction

A motion probe sends out pulses of ultrasound and receives the echoes from objects in front of it. The motion probe can be connected to a CBL and graphing calculator or to a computer with an interface (some motion probes connect directly to a graphing calculator and need no CBL). When the object in front of the motion probe moves, a graph of the motion of the object is displayed on the screen of the calculator. There are several things you should keep in mind as you carry out this investigation:

1. The motion probe (or wall) is the origin or reference point from which distances are measured.
2. The motion probe detects the closest object directly in front of it (including your arms if you swing them as you walk or anything close to your path).
3. The motion probe will not correctly measure anything closer than .5 m. When making your graphs don’t go closer than .5 m from the motion probe.
4. A good way to make the motion graph is to hold the calculator, interface, and motion probe and point the motion probe toward a wall. This will allow you to see the graph on the calculator screen as you walk.

A plot of velocity versus time gives certain information about an object’s motion including how fast and in what direction an object is moving and whether the object is speeding up or slowing down. It is also possible to determine an object’s displacement using a velocity vs. time plot by computing the area underneath the graph during a given interval of time. This property is true for a velocity vs time curve, regardless of its shape.

You will present your findings to the class.

Materials:

Computer interface and software, printer, masking tape, meter stick

Procedure:

Part I: Graphing Position vs. Time

1. Start collecting data. At this point, the motion probe should start ticking and a graph should be drawn on the computer. Try moving back and forth to see what effect this has on the graph.

1. Your group will be assigned one of the qualitative challenges below.

1. Have each group member try the challenge. After several trials show Mr. Beatty. Once he approves your graph you can copy it on the next page.

1. You will then collaborate with a member from each group to get their qualitative graph. You each must explain what you did to produce your graph.

Analysis:

1. Explain the significance of the slope of a distance vs. time graph. Include a discussion of positive and negative slope.

1. What type of motion is occurring when the slope of a distance vs. time graph is zero?

1. What type of motion is occurring when the slope of a distance vs. time graph is constant?

1. What type of motion is occurring when the slope of a distance vs. time graph is changing?

1. Acceleration is the rate of change of speed. When speed is constant acceleration is zero (no change means the rate of change is zero). How does the slope of a distance vs. time graph change when there is acceleration?

1. Describe how a person would have to move to create a distance vs. time graph as pictured.

Part II: The Matching Challenge

1. Open the file “Position vs. Time”. Study it to determine the following:

1. How close should you be to the motion Sensor at the beginning?
2. How far away should you move?
3. How long should your motion last?

2. Walk the graph trying to duplicate the lines as precisely as possible.