Chapter 4 Linear Motion

Position, Distance, and Displacement Position: being able to describe an object’s location is important when things start to move object’s can have positive or negative positions

Position, Distance, and Displacement an object has a positive position if it is to the right of or above the origin (zero point) an object has a Negitive position if it is to the left of or below the origin (zero point) if an object’s position is changing, the object is in motion

Position, Distance, and Displacement Distance & Displacement Definitions: Distance: measurement of the actual path traveled Displacement: the straight-line distance between 2 points with direction

Position, Distance, and Displacement A mouse ran in a curved path from his mouse hole to the cheese. B A 4+4= 8 meters 2 meters 4 meters Which path shows the mouse’s displacement? ____________ Which path shows the distance the mouse traveled? ________ What is the mouse’s displacement? ____________ What distance does the mouse travel? ____________ o After running 4 meters from his hole to the cheese, the mouse returned to his hole (using the same path ). What total distance did the mouse run? ____________ 2-2 = 0 meters What is the mouse’s total displacement? ____________

Notes: Vectors and Scalar Vectors and Scalars: You may have noticed that direction sometimes matters. What are two quantities we have learned about so far where direction matters? Displacement Velocity Vector: If direction matters, we say that the quantity is a vector. Scalar: If direction doesn’t matter, we say that the quantity is a scalar.

4.1 Motion is Relative Motion describes how fast something is going compared to something else. The cars move relative to the track

Motion is Relative cont’ The earth is moving but relative to the earth we are not moving. In a vehicle you are at rest because relative to the vehicle you are not moving

4.2 Speed Speed: If you change positions, it takes time to get to your new position If you care about both the distance traveled and the time it takes, you are concerned with speed. Speed : distance traveled per unit of time

4.2 Speed Speed tells us how Fast an object is moving The units of speed are meters /second The unit is often written with symbols instead: m /s  The definition equation for speed is:

Example If a cheetah is traveling 80 miles per hour That means it travels 80 miles in one hour Speed = 80 miles/1hour

Instantaneous speed This is the speed at any given moment. Your car speedometer measures instantaneous speed.

Average speed If you go on a trip and you estimate how long it will take you may use average speed.  Average Speed: total distance traveled divided by the time it takes to travel that distance  The definition equation for speed is:

Average speed  Sample Problem: o If you traveled 100 m in 50 seconds, what was your average speed? The average speed is?

Average speed Sample Problem: If you traveled 100 m in 50 seconds, what was your average speed? s = ? d = 100 m t = 50 s The average speed is 2 m/s

Units Remember your units do not disappear If you divide miles by hours you get miles/hours for units

4.3 Velocity Velocity is a speed with direction An example of velocity would be 25 m/s West the speed is 25 m/s the direction is West both of these are needed to describe velocity

Constant Velocity This is a constant speed in a straight line Constant velocity cannot turn!

4.4 Acceleration Your Objective: You will be able to compare and contrast Acceleration, Speed and Velocity. You will know the formulas and be able to solve for Acceleration, Speed and Velocity

4.4 Acceleration Acceleration is the rate at which the velocity is changing. Acceleration= change of velocity/time

Changing motion When ever you change your state of motion you are accelerating.

Deceleration This is slowing down. The opposite of acceleration.

Change in Direction When you go around a curve you are always accelerating.

Change in Speed Acceleration can also be the change of speed divided by time. Providing the motion is in a straight line.

4.5 Free Fall Your Objective: You will be able to calculate the speed and distance of an object in free fall.

4.5 Free Fall When something drops straight down it accelerates.

Falling Objects To accelerate under the force of gravity is to free fall. Acceleration of gravity is about 10 m/s*s

Falling Objects The math for the instantaneous speed of falling objects is v = g x t

Rising objects If you throw something straight up two things happen: On the way up it slows down On the way down it speeds up

Rising objects cont At each distance going up and down the speed of the object is proportional.

4.6 Free Fall how far Your Objective: You will be able to calculate the vertical distance an object cover in a given amount of time when in free fall

4.6 Free Fall how far To find the distance of a falling object you need to use the following equation d=1/2 gt 2 This takes in account the acceleration of gravity.

4.6 Free Fall how far

4.7 Graphs and Motion Your objective: To determine an objects motion by Analysis of speed vs. time and distance vs. time graphs.

4.7 Graphs and Motion Speed vs. Time graphs v is on the y axis t is on the x axis The slope of the line will be the Acceleration.

Graphs cont. Distances vs. time d is on the y axis t is one the x axis Free fall will make a curved line This is because t is squared (d=1/2g*t2)

4.7 Graphs and Motion

4.8 Air Resistance Air resistance slows down how fast an object falls. The air is pushing slightly up causing the object to slow.