Chapter 4 Linear Motion

How do we determine if an object is in motion?

Observing Motion Motion An object’s change in position relative to a reference point When an object changes position with respect to a frame of reference, the object is in motion. north, south, east, west, up, or down

Group Questions Slide 1 A person sits in the passenger seat of a car that is traveling down a street. Describe the person as seen by each of the following observers: A person sitting in the backseat of the car A person standing on the sidewalk as the car passes The driver of a second car moving in the same direction and passing the first car

Group Questions Slide 2 A person stands near a bus stop. Describe the standing person’s motion as seen by the following observers: A person sitting in an approaching bus A person riding in a car moving away from the bus stop Another person standing at the bus stop

Discussion Do any observers say that the person sitting in the passenger seat of the car in the first slide was moving? Explain Do any observers say that the person sitting in the passenger seat of the car in the first slide was not moving? Explain Do any observers say that the person standing near the bus stop in the second slide was moving? Explain Do any observers say that the person standing near the bus stop in the second slide was not moving? Explain Based on these answers, explain what it means when someone says an object is “moving.”

Observing Motion Motion requires an object moving over a distance or how far it has moved. When an object moves displacement takes place.

Distance vs Displacement What is the difference between distance and displacement? Which should you use when calculating how many gallons of gas you will need for a road trip? Which does the saying “as the crow flies” refer to?

Speed Speed tells you how fast something traveled over specific time. Speed is calculated as distance d divided by time t. s=d/t Speed can also be measure in small spurts called instantaneous speed. Ex. Speedometer in a car

Problem Situation I have dinner reservations at 8 pm at the Spaghetti Warehouse in Marietta off of exit 259. I just got on I-75 South from Barrett Parkway at exit 269. Assuming the distance from here to there is 10 miles, and it is now 7:50 pm, how fast must I drive to make my reservation? I know that Speed equals distance divided by time Distance is 10 miles Time is 10 minutes Speed = distance = 10 miles = 1 mile / minute! time 10 minutes

Total Distance Covered Helpful Hint Average Speed = total distance covered travel time Total Distance Covered D S T Average Speed Total Time

Velocity Velocity not only tells you the speed of an object but it also tells the direction. When velocity is calculated you use the same equation as speed, but you must specify direction.

Problem It takes you 60 mins to travel 2km, what is your average speed?

Graphing Motion A graph can be used to study motion Distance – Time graph x-axis= time y-axis= distance The slope of the line is the speed

Practice Make a line graph of the data of a runner. Determine the during which time interval the runner is moving faster, moving slower, and standing still. Explain the relationship between the slope of the line and the runner’s speed. Time (s) Position (m) 10 20 30

Answer

Motion Diagram

6 m 5 m 4 m 3 m 2 m 1 m Distance 3 s 2.5 s 2 s 1.5 s 1 s .5 s Time Position versus Time 7 Position (meters) 5 3 1 1 2 3 Time - (seconds)

Question? Which line shows the object covering the most ground in a certain amount of time? Position versus Time Position End of Lecture was here Time

Some Names?? We call the distance an object travels in a certain amount of time “speed” Speed = Distance covered Time Two Types of Instantaneous Average

Distance over Time is ? Distance versus Time 7 Distance (meters) 5 1 2 Time - (seconds) 1 2 3 Distance versus Time 5 7 Distance divided by time on this kind of graph is the: ___________ of the object ___________ of the line

Question? Which line shows the object covering the most ground in a certain amount of time? Position versus Time Position Time

Question? Which object has the highest rate of speed or rather, which object is moving the fastest? Position versus Time Position Time

Question? Rank the five colors in order from slowest to fastest. Position versus Time Position Time

Changes Velocity is Speed + Direction How can we change our speed? How can we change our velocity?

Acceleration Whenever your speed or direction changes you accelerate. Calculate acceleration a= vf-vi/t

Think about it Think about your daily life. List 5 examples of acceleration. Classify each example of acceleration as an increase in speed, a decrease in speed, a change in direction, or a combination.

Is your friend right? Your friend Lynn is getting frustrated that y’all are driving in circles [literally] trying to find the store. Lynn looks at the speedometer, sees its not moving from 25 mph and says: “Well, at least we are not accelerating while driving around the around the mall.” What do you say to Lynn?

Revisit Motion Diagrams Spacing between dots represent what? Arrows represent what two things? If the object started to move faster towards the left, what would the diagram look like now?

Check your representation skills! Construct a motion diagram for the ball in this video! Video

Discuss with neighbor Which diagram below resembles your diagram the most? C D A B

Discuss with neighbor In what direction is your CHANGE in velocity for that video/motion diagram? C A B Change in velocity is zero

Discuss with neighbor In what direction is your CHANGE in velocity for that video/motion diagram? C A B Change in velocity is zero

Motion Diagram Combine the two and you get: Dv

Create a story Devise a story for an object whose motion is consistent with the motion diagram. Dv Dv = 0 Dv

Create a story Dv Devise a story for an object whose motion is consistent with the motion diagram to the right. Dv Dv = 0

Throw the ball up now? We just did a motion diagram for a ball on its way down. Imagine, if I throw the ball up in the air? What does a motion diagram look like for the ball while it is moving upwards? While its at the top?

Example Problem I am standing on a cliff and I drop a rock from rest. After two seconds, the rock is moving at a speed of 20 m/s. What is the rate of acceleration for this rock? I know that acceleration equals change in velocity per unit time Change in Velocity is 20 m/s Time is 2 seconds Acceleration = D velocity = 20 m/s = 10 m/s/s or time 2 s 10 m/s2

Question If I can accelerate at a rate of 15 mph per second, how long will it take me to accelerate from 30 to 90 miles per hour?

Question If I can accelerate at a rate of 15 mph per second, how long will it take me to accelerate from 30 to 90 miles per hour? 2 seconds 4 seconds 8 seconds 900 seconds

Question You are in your car going 75 mph. If you can decelerate your car at a rate of 25 mph per second, then how long does it take you to stop your car?

Question You are in your car going 75 mph. If you can decelerate your car at a rate of 25 mph per second, then how long does it take you to stop your car? 100 seconds 1/3 second 3 seconds 50 seconds What is the direction of the objects acceleration compared to the velocity of the car?

Problem A flowerpot falls off a second-story windowsill. The flowerpot starts from rest and hits the sidewalk 1.5s later with a velocity of 14.7m/s. Find the average acceleration of the flowerpot.

Mathematical Representations learned thus far v = Dd / Dt = velocity equals change in displacement over change in time a = Dv / Dt = acceleration equals change in velocity over change in time Free Fall Only Starting at Rest!!!!!!! a = g = 10 m/s2 [actually 9.8 m/s2] v = g t = velocity is g multiplied by time d = ½ g t2 = distance is one half multiplied by g multiplied by times squared.