Chapter 10

Motion Notes

Definition of position

• An object’s location

Definition of Reference Point

• A location to which another location is compared

Definition of motion

• A change of position over time.

Ch. 10.1 An Object in Motion Changes Position

• I. Position describes the location of an objectA. Describing a position

1. A reference point is a location to which you compare other locations

2. Longitude and latitude help make it easy to compare locations

reference point

motion

position

An object in motion changes position.

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Position is measured from a reference point.

Motion is measured relative to an observer.

startingposition

endingposition

10.110.1

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Measuring Motion• Speed is the distance an object travels in a

certain amount of time• Speed = distance divided by time• S = d/t d = s(t) t = d/s• Velocity is both speed and direction (v = d/t)• Speed and velocity are often interchanged

but velocity involves direction

II. Motion is a change in position

• 6. What provides evidence that motion has happened?

• A change in position

B. Relative Motion

8. If you are seated on the train, who or what would be moving compared with you?

• The person outside, the suitcase, and the ground would be moving

• Who would be still compared to you?

• The people inside would be still.

B. Relative Motion

9. If you are standing outside the train, who or what would be moving compared with you

• The people in the train and the train would be moving

• Who or what would be still?

• The ground and the suitcase would be still.

10. Summarize the meaning of relative motion.

• Relative motion is the concept that the motion an observer sees depends on the observer’s frame of reference. Observers in different reference frames see different motions for the same object.

Section 10.2

Speed measures how fast position changes

Definition of speed

• A measure of how fast something moves through a particular distance over a definite time period.

Definition of velocity

• A speed in a specific direction.

Definition of Vector

• A quantity that has both size and direction.

• Speed is how fast positions change with time.

velocity

vector

speed

Speed measures how fast position changes.

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distance

00:00 00:02Speed =distance

time

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• Speed is how fast positions change with time.

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• Velocity is speed in a specific direction.

Velocity

velocity

vector

speed

Speed measures how fast position changes.10.210.2

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A. Calculating Speed• I. Position can change at different rates.– A. Calculating speed

• Requires both distance and time• Formula is S = d/t

–a. S stands for speed Units: km/h m/h m/s–b. D stands for distance Units: meters(m) kilometers

(km), miles (mi)–C. T stands for time Units: seconds (s), hours (h),

minutes(min)

3. How does the unit for speed (m/s) relate to the formula for

speed?The unit for speed shows a distance

unit, the meter, divided by a time unit, the second, as does the formula

Steps for Solving Problems

• What do you know?

• What do you want to find out?

• Write the formula

• Substitute into the formula

• Calculate and Simplify

• Check that your units agree

• Answer – Circle your answer

B. Average Speed 4. If someone ran 100

meters in 20 seconds, what is her speed?

D = 100 mT = 20 sS = ?S = d/tS = 100m/20sS = 5 m/s

B. Average Speed 4. If someone ran 100 meters

in 20 seconds, then ran another 100 meters in 25 seconds, what would the runner’s average speed be over the whole 200 meters?

D = 200mT = 20 +25 = 45 sS =?S = d/tS = 200 m/45sS = 4.4 m/s

Constant and Average Speed

• Constant speed means equal distances in equal amounts of time.

– Represented by a straight line on a graph

• Average Speed = total distance divided by total time.

C. Distance-Time Graphs5. The distance-time graph

below shows the motion of a cat. During the 100 seconds shown, the cat was walking, running, and resting. Label each line segment of the graph with a description of the cat’s motion. Explain your answer. 0-40 seconds – walking, cat is moving slowly; 40-60 seconds – resting, cat is not moving; 60-100 seconds – running, cat is moving quickly

II. Velocity includes speed and direction.

• Velocity– Need to know speed and direction– Changing either speed or direction causes a

change in velocity– Is considered a vector because it has both size

and direction– Represented graphically by an arrow

A-B. Velocity, Velocity versus Speed

• 7. Explain why velocity is a vector but speed is not.– A vector is a quantity that has both size and

direction. Velocity is a vector because it is a measure of both speed, which has a size, and direction. Speed is only a measure of a size, so it is not a vector.

Centripetal Acceleration

• An object moving in a circle or curve is constantly changing direction therefore it is accelerating (centripetal acceleration)

• Centripetal acceleration is always towards the center of a circle.

Energy and Change

• Energy is the ability to do work

• Two Types of Energy

– Potential (PE)– stored energy

• Associated with the position of an object

– Kinetic (KE) – energy of motion

• Depends on an objects mass & speed.

Gravitational PE

• Gravitational Potential energy is abbreviated: GPE

• It depends on an object’s weight and the distance it falls before stopping completely

Law of Conservation of Energy• The Law of Conservation of Energy states

that energy cannot be created or destroyed. The total amount of energy always remains the same, but it can change form

• Example:– At the top of the hill the rock as Potential

Energy– As it falls the rock loses potential energy

and gains kinetic energy

Section 10.3

Acceleration measures how fast velocity changes.

Acceleration• Acceleration is the rate at which velocity changes

over time.• It is a change in velocity resulting from speeding up,

slowing down, or changing direction• Acceleration = change in velocity divided by time• Formula: a = (vf – vi)/t

– Vf = final velocity (ending speed)– Vi = initial velocity (starting speed)– t = time (amount of time it takes to start/stop)

seconds(s), hours (h), minutes (min)

Acceleration (Cont.)

• Negative acceleration (deceleration) is a decrease in velocity over time. (slowing down)

• Any change in velocity is acceleration even if the speed remains the same.

• Acceleration in the Same Direction as Motion

Acceleration measures how fast velocity changes.

acceleration

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• Acceleration in the Opposite Direction of Motion

• Acceleration at a Right Angle to Motion

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A. Calculating Acceleration

4. What is the formula for acceleration?

acceleration = final velocity – initial velocity

time

What units are used for each of the values?

Unit for time = seconds (s)

Unit for velocity = m/s

Unit for acceleration = m/s2

A. Calculating Acceleration

5. A skater begins skating at a velocity of 1 m/s. After 4 seconds, her velocity is 3m/s. What is the skater’s acceleration? Show your work.

Vi = 1 m/sVf = 3 m/sT = 4sA = ?a = vfinal – v initial ;a = 3 m/s – 1 m/s; a = 0.5 m/s2

time 4s

B. Acceleration over Time6. A car has an acceleration of 4 m/s2. What will

the increase in its velocity be after 2 seconds? If it started with a velocity of 30 m/s, what is its final velocity?

A = 4 m/s2

T = 2 sVi = 30 m/sA = vf – vi/t 4m/s2= vf – 30/24(2) = (vf – 30) = 8 m/s; vf = 8 + 30 = 38 m/s

C. Velocity-Time Graphs

• 7. Fill in the velocity-time graph to show the velocity of a ball rolling at a constant speed of 7 m/s for 5 seconds.