Vocabulary Term Definition Distance Displacement Position Average Speed Average Velocity Instantaneous Speed Acceleration Page 1
Homer walked as follows: Starting at the 0,0 coordinate, he walked 12 meters east, 8 meters west, 10 meters east. West -18-16 -14-12 -10-8 -6-4 -2 0 2 4 6 8 10 12 14 16 18 East His displacement was 14 meters east. His distance traveled was 30 meters. His final position was +14 meters. Using this information, define the following: Displacement Distance Position Check Questions What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school? What distance did the cross-country team run? Sketch your own example of a situation where a person/object walks in three different directions and has a different displacement, distance, and position Page 2
Peter Griffin needs to purchase a new tv. He resets his odometer when he leaves his house heading South. When he arrives at Best Buy, the odometer reads 30 miles. It took him exactly one hour to get there. His average speed was 30 miles/hour. His average velocity was 30 miles/hour SOUTH. Using this information, define the following: Average speed Average velocity Peter reset his odometer to come home. Again it was exactly 30 miles and it took him 1 hour. His average speed for the entire trip was 30 miles/hour. His average velocity was 0 miles/hour. Using this information, revise the above definitions: Average speed Average velocity What is the basic difference between speed and velocity? Page 3
Cartman took a trip South to Saddle River. He reset his odometer at the beginning of the trip. When he arrived in Saddle River the reading on the odometer was 100 miles. The entire trip took 4 hours. Solve the following. 1) What total distance did he travel? 2) What was his displacement? 3) What was his average speed? 4) What was his average velocity? Page 4
Section 1.3 Speed (pages 17-21) Speed What is it? (definition) Measurement Symbol Units Speed s Meters/second Distance d Meters time t seconds Page 5
Velocity What is it? (definition) Measurement Symbol Units velocity v Meters/second displacement d Meters time t seconds 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 Page 6
Speed & Velocity Examples 1. A football field is about 100 m long. If it takes Anthony 20 seconds to run its length, how fast (what speed) was he running? speed displacement = time = s=d/t 2. Calculate the average speed of a car stuck in traffic that drives 12 kilometers in 2 hours. 3. Crystal travels 60 kilometers South in 30 hours on her bicycle. What is her average velocity? 4. How far will David travel if he runs for 10 minutes at 2 m/sec? 5. If Brielle travesl a distance of 750 miles in 10 hours, what is her average speed? Page 7
6. Calculate the distance that Carina runs if she maintains an average speed of 45 km/hour for 2 hours. 7. Sketch your own example of a situation where a person/object travels with the same average speed and average velocity. 8. Sketch your own example of a situation where a person/object travels in two different directions and has a different displacement and distance. Page 8
Acceleration What is it? (definition) v = v f - v i If an object is accelerating then it is either Measurement Symbol Units acceleration a meters/second 2 Change in velocity v meters/second time t seconds Acceleration Examples Page 9
1. Summer increases her velocity from 2.0 m/s to 10.0 m/s North in 3.0 seconds. What is Summer s acceleration? Acceleration of Beginning speed = 2.0 m/s the skater Final speed = 10.0 m/s Change in time = 3 seconds The acceleration of the skater is 2.7 meters per second per second North or 2/7 m/s 2. 2. A car accelerates at a rate of 3.0 m/s 2 South. 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? The time to reach the final speed. Beginning speed = 8.0 m/s; Final speed = 25.0 m/s Acceleration = 3.0 m/s 2 The time for the car to reach its final speed is 5.7 seconds. 3. While traveling along a highway Erica slows from 24 m/sec to 15 m/sec East in 12 seconds in her car. What is the Erica s acceleration? Acceleration V2=15 m/s V1=24 m/s t=12s 4. A parachute on a racing dragster opens and changes the speed of the car from 85 m/sec to 45 m/sec West in a period of 4.5 seconds. What is the acceleration of the dragster? V2=45 m/s V1=85 m/s t=4.5s 5. The cheetah, which is the fastest land mammal, can accelerate from 0.0 m/s to 33 m/s East in 3.0 seconds. What is the acceleration of the cheetah? Page 10
6. The Lamborghini Diablo sports car can accelerate from 0.0 m/s to 44 m/s North East in 4.0 seconds. What is the acceleration of this car? 7. A helicopter s speed increases from 25 m/sec to 60 m/sec West in 5 seconds. What is the acceleration of this helicopter? 8. Which has more acceleration when moving in a straight line a car increasing its speed from 75 to 90 km/h, or a bicycle that goes from zero to 15 km/h in the same time? Defend your answer. 9. Sketch your own example of a situation where a person/object is accelerating. (Draw a picture and create a short story to accompany your picture) Page 11
d d v s t v t a t Class Work 1. What is the average speed of a cheetah that sprints 100 m East in 4 s? 2. a. Paige makes one lap around a 400 m track in a time of 25.0 s. What was Paige s average speed? b. What is Paige s average velocity? (Hint: Reread the definition for velocity.) 3. A soccer field is about 120 m long. If it takes Sarah 10 seconds to run its length, what is her average speed? 4. Calculate the average velocity of a car that drives 50 meters North East in 25 seconds. 5. 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? 6. Dylan ran 5000 meters from the cops and an average velocity of 6 meters/second West before he got caught. How long did he run? Page 12
d d v s t v t a t Group Work 7. 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? 8. Samantha runs a 400 m lap in 53.5 s. What is her average speed? What is her average velocity? 9. What is the average speed of a car that traveled 300.0 meters North West in 3600 seconds? What is the cars average velocity? 10. 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? Page 13
d d v s t v t a t 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? 2. A bullet travels with an average velocity of 850 m/s. How long will it take a bullet to go 1000 m? 3. Every summer Mr. Magoo drives to Michigan. It is 3900 m to get there. If he drives with an averagespeed 100 m/s, how much time will he spend driving? 4. What is the average speed of a cheetah that travels 200.0 meters South in 4.0 seconds? What is the cheetah s average velocity? 5. After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner s acceleration? Page 14
Challenge Problems 1. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Jillian 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 Jillian sprints its 60.0 m length at a speed of 5.00 m/s. Does Jillian make it to class on time or does she get detention for being late again? Show all of your work. First Hallway Given Formula Set-up Solution Second Hallway Given Formula Set-up Solution Final Hallway Given Formula Set-up Solution 2. 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? Given Formula Set-up Solution 3. 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. Mr. Menzella runs the race in 10.40 s. Mr. Beatty 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? Page 15
Eva recorded the position of a motorized toy car using the origin as her reference point. She wrote this in the table below. Notice how she labeled the columns using physical quantities that she measured versus the units used. Did You Know? Physical quantity: A tangible property that can be measured with a special instrument in specific units. For example, one unit for the physical quantity time t is a second. Change in a quantity: Often, in science and mathematics, we are interested in the change in a quantity. The symbol is used to represent change. For example, Temperature 2 Temperature 1 = T. Here Temperature2 stands for the temperature measured at some clock reading 2 which occurred after clock reading 1 when Temperature 1 was measured. a) What patterns do you see in the data? b) Explain the meaning of each column in the table. Make sure to specify the difference between the columns. c) If you were to plot a graph of position vs. time what would you title the graph? Which variable would you place on the x and y-axes? Title: Page 16
Match the physical quantities with the units from the list below (a quantity can be measured in different units): mass, meter, temperature, second, foot, year, centimeter, gram, kilogram, celsius, position, time interval, hour Physical Quantity Possible Units Temperature Degrees Celsius Represent the motion of the ball from Eva s experiment with a graph. IN other words, plot the points below on the position-versus-clock reading graph and draw a trend line. (plot the points on graph 1) Clock Reading Position 0 0 1 2 2 4 3 6 4 8 Graph 1 Page 17
Now create two additional position-versus-time graphs using the tables below. In the first table Eva recorded the position of a toy car rolling down a ramp toward her. In the second table Eva recorded the position of a toy car as it slows to a stop in front of her. Graph 2 (use the information from the above data table) 1 2 3 4 Page 18
Clock Reading t Position x Time interval t Change in position x 0 s 16 cm ----- ----- 1 s 23 cm 1 s 0 s = 1 s 23 cm 16 cm = 7 cm 2 s 28 cm 2 s 1 s = 1 s 28 cm 23 cm = 5 cm 3 s 31 cm 3 s 2 s = 1 s 31 cm 28 cm = 3 cm 4 s 32 cm 4 s 3 s = 1 s 32 cm 31 cm = 1 cm Graph 3 1 2 3 4 What are the differences in the motion of the cars for the three experiments Eva performed? a) What are the differences between the three graphs? (Specifically comment on what s happening to the line.) b) Develop a testable hypothesis that relates type of motion to graphical appearance (how the graph looks). Did You Know? Position, displacement, distance, and path length: These refer to different things! Position x is the location of an object relative to a chosen zero on the coordinate axis. Displacement x2 - x1 indicates a change in position and has a sign indicating the direction of the displacement. The magnitude of that position change is the distance and is always positive. Path length refers to the total length of the path that was travelled. Page 19
Time: The clock reading or time (t) is the reading on a clock, on a stopwatch, or on some other time measuring instrument. Time can be measured in many different units, such as seconds, minutes, hours, days, years, and centuries, etc. In SI system it is measured in seconds. Time interval: The difference between two clock readings is the time interval. If we represent one time reading as t1 and another reading as t2 then the time interval between those two clock readings is t2 - t1. Another way of writing this statement is: Change: The symbol Δ is the Greek letter delta and in physics and mathematics it reads as delta t (Δt) or the change in t. Use the graph to record data into the table provided. Clock Reading Position Time Interval Δt 0 1 2 3 4 Change in position Δx Page 20
You should notice that the two physical quantities in the graph did not have units of measure with them. Describe a real life situation for this motion if the units of measure were kilometers and hours. Describe another situation if the units were meters and seconds. Draw a picture for each of the situations you described above. Hypothesize Let s review position versus time graphs. Use what you learned in the previous lesson to help you develop the following rules. a) What does constant pace motion look like on a position versus time graph? b) What does speeding up motion look like on a position versus time graph? c) What does slowing motion look like on a position versus time graph? Use the graphs and descriptions below to test your rules. a) This graph represents an object moving at constant pace. Does this match your rule for constant pace? Explain why or why not. Modify your rule if necessary. Page 21
b) This graph represents a slowing object. Does this match your rule for slowing? Explain why or why not. Modify your rule if necessary. c) This graph represents an object speeding up. Does this match your rule for speeding up? Explain why or why not. Modify your rule if necessary. Page 22
Examine the graphs below and then answer each of the questions below by recording the associated letters on the line provided. a) Which graphs represent objects moving at constant pace? b) Which graphs represents objects speeding up? c) Which graphs represent objects that are slowing? d) Which graphs represent an object moving in the negative direction? e) Do any of the graphs show an object that is not in motion? How do you know? Can we consider this a constant pace? Examine the Position vs. Clock Reading graph for a football player running a play below. Create a story to describe the motion of the player in words using the graph above. Page 23
Use the graph above and calculate the slope of the line for each case. Explain how you calculated the slope. Need Some Help? Slope: Often used to describe the measurement of the steepness of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the change in the value of the dependent variable (vertical change) over the change in the value of the independent variable (horizontal change). In other words, vertical change divided by horizontal change! a) For the skiers, what do you think the slope of the line represents? Try to answer using your common sense. b)what are the units of slope? How do you know? c) Refer to the graphs to check if your answer makes sense. How do you know? Is there anything else you notice? Explain. Page 24
Qualitative graphs x (m) (m/s) t (s) t (s) x (m) (m/s) t (s) t (s) x (m) (m/s) t (s) t (s) Page 25