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

Motion is Relative Although you may be at rest relative to Earth’s surface, you’re moving about 100,000 km/h relative to the sun.

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 - how fast an object is moving. Any combination of units for distance and time that are useful and convenient are legitimate for describing speed: miles per hour (mi/h) kilometers per hour (km/h) centimeters per day light-years per century

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

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

Acceleration Accelerate in the direction of velocity–speed up

Accelerate in the direction of velocity–speed up 4.4 Acceleration Accelerate in the direction of velocity–speed up Accelerate against velocity–slow down

Accelerate in the direction of velocity–speed up 4.4 Acceleration Accelerate in the direction of velocity–speed up Accelerate against velocity–slow down Accelerate at an angle to velocity–change direction

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?

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

4.4 Acceleration think! Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then from 45 to 50 km/h. What is its acceleration?

4.4 Acceleration think! Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then from 45 to 50 km/h. What is its acceleration? Answer: The speed increases by 5 km/h during each 1-s interval in a straight line. The acceleration is therefore 5 km/h•s during each interval.

4.4 Acceleration think! In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle?

4.4 Acceleration think! In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle? Answer: The car and truck both increase their speed by 15 km/h during the same time interval, so their acceleration is the same.

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?

Free Fall Acceleration Gravity causes things to accelerate to the ground. All things fall with the same acceleration: The acceleration from gravity is 10m/s2=g

4.5 Free Fall: How Fast If a falling rock were somehow equipped with a speedometer, in each succeeding second of fall its reading would increase by the same amount, 10 m/s.

4.5 Free Fall: How Fast

Free Fall velocity? You jump from the second story building and hit the ground 2 seconds later. How fast were you falling when you hit the ground?

4.5 Free Fall: How Far think! As you throw a ball up in the air does the ball’s velocity, increase, decrease, or stay the same? If you throw a ball up is the ball slowing down or speeding up? Should your velocity be higher or lower? If the ball has an initial velocity of 20 m/s, what is the balls velocity after 1 second?

If you throw a ball up is the ball slowing down or speeding up? 4.5 Free Fall: How Fast think! If you throw a ball up is the ball slowing down or speeding up? As you throw a ball up in the air does the ball’s velocity, increase, decrease, or stay the same? Should your velocity be higher or lower? If the ball has an initial velocity of 20 m/s, what is the balls velocity after 1 second? Answer: Slows Down. If the ball is slowing down, that means the velocity is decreasing. Our velocity should be lower. Acceleration decreases velocity by 10m/s every second. 20m/s – 10m/s= 10m/s

4.5 Free Fall: How Fast The change in speed each second is the same whether the ball is going upward or downward.

4.5 Free Fall: How Far For each second of free fall, an object falls a greater distance than it did in the previous second.

How far does an object in free fall travel in the first second? 4.5 Free Fall: How Far How far does an object in free fall travel in the first second? What is your Initial speed before you drop the object? What is the instantaneous speed after 1 second? Using answer 1 and 2, what is the average speed? Using the distance, time, speed triangle: find distance.

How far does an object in free fall travel in the first second? 4.5 Free Fall: How Far How far does an object in free fall travel in the first second? The initial speed is 0 m/s. At the end of the first second, the falling object has an instantaneous speed of 10 m/s. The average speed is 5 m/s. During the first second, the object has an average speed of 5 m/s, so it falls a distance of 5 m.

4.5 Free Fall: How Far

4.5 Free Fall: How Far These distances form a mathematical pattern: at the end of time t, the object starting from rest falls a distance d.

4.5 Free Fall: How Far think! An apple drops from a tree and hits the ground in one second. What is its speed upon striking the ground? What is its average speed during the one second? How high above ground was the apple when it first dropped?

4.5 Free Fall: How Far think! An apple drops from a tree and hits the ground in one second. What is its speed upon striking the ground? What is its average speed during the one second? How high above ground was the apple when it first dropped? Answer: The speed when it strikes the ground is 10 m/s. The average speed was 5 m/s and the apple dropped from a height of 5 meters.

Air Resistance and Falling Objects Drop a feather and a coin and the coin reaches the floor far ahead of the feather. Air resistance is responsible for these different accelerations. In a vacuum, the feather and coin fall side by side with the same acceleration, g. Vacuum- Not what we use to suck up dirt in our homes….its when scientists remove ALL air (matter) from an area.

Air Resistance and Falling Objects A feather and a coin accelerate equally when there is no air around them.

How Fast, How Far, How Quickly How Fast Changes IMPORTANT!!!!! One of the most confusing concepts encountered in Physics is acceleration, or “how quickly does speed or velocity change.” What makes acceleration so complex is that it is a rate of a rate. It is often confused with velocity, which is itself a rate (the rate at which distance is covered). Acceleration is not velocity, nor is it even a change in velocity.

How Fast, How Far, How Quickly How Fast Changes Don’t mix up “how fast” with “how far.” How fast something freely falls from rest after a certain elapsed time is speed or velocity. The appropriate equation is v = gt. How far that object has fallen is distance. The appropriate equation is d = 1/2gt2.

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.