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MOTION, DISTANCE, AND DISPLACEMENT

Q: What is motion?

A: Motion is any change in the position or place of an object. ________________ is the study of

motion (without considering the cause of the motion).

Distance vs. Displacement

- Distance

- Distance is the length an object travels along a path between two points.

- Metric unit for distance = ________________

- Displacement

- Displacement consists of two parts

1) How far the object is from its starting point

2) The _____________________________________________________________________________

- Displacement is often used when giving directions

- Compare these two directions: walk 5 blocks vs. walk 5 blocks north. Which directions give

you a better of idea of where to go?

Practice Problem #1:

Think about the motion of a roller coaster car...

1) If you measure the path along which the car has traveled, you have measured the ___________.

2) If you consider the direction from the starting point to the car and how far the car is from where it

started, you have measured the ________________.

3) What is the car’s displacement after one complete trip around the track? ________________

- Displacement is an example of a vector

- A vector is a quantity that has ________________ and ________________

- The magnitude can be size, length, or amount

- We represent vectors on a graph or map with arrows

- The length of the arrow is equal to the ______________________________________________

- You can add displacements using vector addition (combining vector magnitudes and directions)

- For displacement along a straight line:

Two displacements represented by

two vectors in the same direction

can be ________________ to one

another (Figure A)

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For two displacements in opposite

directions, the magnitudes

________________ from one another

(Figure B)

- For displacements that aren’t along a straight path

For two or more displacement vectors in

different directions, you can combine by

graphing

The picture shows yellow vectors representing a

boy’s path walking from home to school. The

total distance walked is __________ blocks.

The vector in red represents the boy’s total

displacement. Measuring this vector gives a

displacement of about __________ blocks.

________________________________________________________________________________________

SPEED

Q: How can we tell how fast an object is moving?

A: By calculating its speed.

- Speed is the distance an object travels in a certain period of time

- Metric unit for speed = meters/second (m/s) or kilometers/hour (km/hr)

- We can look at speed in two ways:

1) __________________________________

How fast an object is moving at any given moment in time

Speed measured at a particular instant

Ex: A speedometer in a car tells us instantaneous speed

Ex: A radar gun used by the police to determine whether or

not you are speeding while driving

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2) __________________________________

Average speed for the entire duration of a trip

Average speed = Total Distance Total Time

OR s = d/t

SPEED EXAMPLE PROBLEM:

John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?

Step 1: What information are you given?

Step 2: What unknown are you trying to calculate?

Step 3: What formula contains the given quantities and the unknowns?

Step 4: Replace each variable with its known value and solve.

Step 5: Does your answer seem reasonable?

Practice Problem #2: While traveling on vacation, you measure the times and distances traveled. You travel 35 km in 0.4 hours, followed by 53 km in 0.6 hours. What is your average speed?

d s t

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Practice Problem #3: It takes you 45 s to walk 72 m down the block to your friend’s house. What is your average speed? __________________________________________________________________________________________

GRAPHING SPEED

Q: How can we visually represent the speed of an object?

A: A good way to describe speed is with a distance-time graph.

- Graphing Constant Speed

- Constant Speed: When an object’s speed doesn’t change

Ex: A race car with a constant speed of 96 m/s travels 96 meters every second

- Graph of constant speed is a straight, diagonal line

- When the motion of an object is graphed by plotting the distance it travels versus time, the

________________ of the resulting line is the object’s ________________

Slope = (y2-y1) Choose two points on the line and plug the (x2-x1) coordinates into the formula

Practice Problem #4: Draw a distance(position) – time graph for a person walking a constant SLOW speed. Draw your guess

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Observe the demonstration and draw the ACTUAL GRAPH of a person walking slowly below:

Practice Problem #5: Draw a distance(position) – time graph for a person walking a constant FAST speed. Draw your guess

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Observe the demonstration and draw the ACTUAL GRAPH of a person walking quickly below:

- Graphing Varying Speed

- Varying Speed: When an object travels at different speeds during different parts of a trip

Ex: A car travels 10 m/s for 60 s then travels 20 m/s for the next 120 s

- Slopes of the different parts of the trip can be calculated individually using the formula above

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Practice Problem #6: Draw a distance-time graph of an object traveling at a constant slow speed for 4 seconds, stopping for 2 seconds, then traveling at a constant fast speed for 4 seconds. Observe the demonstration and then draw the actual graph below:

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Practice Problem #7: Answer the following questions about the graph to the right: 1) Which of the objects are moving at a constant

speed? 2) Which object is traveling the fastest? How do you

know? 3) Which object is traveling the slowest? How do

you know?

__________________________________________________________________________________________

VELOCITY

- Velocity is the _________________________________________ in which an object is moving

- Velocity gives a more complete description of motion than speed alone

- You solve for velocity the same way you solve for speed

Speed = distance Velocity = distance & direction time time

Ex: 25 km/hr Ex: 25 km/hr west

- The direction of motion can be described in various ways:

North, south, east, west

_______________________________________

Positive vs. negative

VELOCITY EXAMPLE PROBLEM: What is the velocity of a rocket that travels 9000 meters away from the Earth in 12.12 seconds?

Step 1: What information are you given?

Step 2: What unknown are you trying to calculate?

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Step 3: What formula contains the given quantities and the unknowns?

Step 4: Replace each variable with its known value and solve.

Step 5: Does your answer seem reasonable?

Practice Problem #8: Find the velocity of a swimmer who swims exactly 0.110 km toward the shore in 0.02 hr. Practice Problem #9: Find the velocity of a baseball thrown 38 m from third base toward home plate in 1.7 s. _________________________________________________________________________________________

ACCELERATION

Q: How can we determine if there has been a change in the velocity of an object?

A: By calculating the object’s acceleration

- Acceleration is a ________________________________________________

- Since velocity includes both speed and direction, acceleration occurs if there is a change in

speed, a change in direction, or a change in both

- Metric unit = _____________________

Ex: A dog chases its tail – direction is changing so the dog is accelerating

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Ex: A car slows down when it sees a red light – speed is changing so the car is accelerating

Ex: A car sets its cruise control and continues to head east – the speed and direction stay the

same, so the car is NOT accelerating

Ex: You drop a ball off the roof of a tall building and it speeds up as it falls – speed is

changing at a rate of 9.8 m/s2, so the ball is accelerating

- Society often uses the term acceleration to describe situations in which the speed of an object is

increasing

- Scientifically, however, the change may be an increase OR a decrease in speed

Acceleration is ______________________________________________

Positive acceleration = speeding up

Negative acceleration (deceleration) = _________________________

- In addition, an object can accelerate even if the speed remains ______________

Ex: Riding a bike around a curve

o Although the speed remains constant, the change in direction

means that you are accelerating

o This is known as __________________________________

Ex: You can also think of a carousel

o The speed of the carousel remains constant throughout the

ride, but the carousel is constantly changing direction

o This means the carousel is _______________________

- Constant Acceleration: A steady change in velocity of an object moving in a straight line

Velocity changes by the same amount each second

- Calculating Acceleration

Acceleration = a = Change in velocity = (vfinal – vinitial) Total time t

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ACCELERATION EXAMPLE PROBLEM:

A dragster in a race accelerated from stop to 60 m/s by the time it reached the finish line. The dragster moved in a straight line and traveled from the starting line to the finish line in 8.0 s. What was the acceleration of the dragster?

Step 1: What information are you given?

Step 2: What unknown are you trying to calculate?

Step 3: What formula contains the given quantities and the unknowns?

Step 4: Replace each variable with its known value and solve.

Step 5: Does your answer seem reasonable?

Practice Problem #10: A ball rolls down a ramp starting from rest. After 2 seconds, its velocity is 6 m/s. What is the acceleration of the ball?

Practice Problem #11: A flower pot falls off a second story windowsill. The flower pot starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the flower pot.

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__________________________________________________________________________________________

GRAPHING ACCELERATION

- You can use a ____________________________to display and calculate acceleration

- The slope of a velocity-time graph is equal to ________________________________

- Velocity-time graphs are linear graphs

- Another way to represent acceleration and velocity is through a _____________________________

A ticker tape analysis is one way to do this

Marks are placed on a long tape at regular intervals of time

The trail of dots gives a history of an _________________________________

This graph shows positive acceleration An airplane taking off from the runway increased its

speed at a constant rate because it was moving up into the sky with constant acceleration

This graph shows negative acceleration Constant negative acceleration decreases speed Imagine a bicycle slowing to a stop The horizontal line segment represents

_____________________________________________ The line segment sloping downward represents the

bicycle slowing down In this case, the change in speed is negative, so the

slope of the line is ____________________________

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The distance between

the dots represent the object’s position change during that time interval

o A large distance means the object was moving ___________________

o A small distance means the object was moving ___________________

Based on the dots on a ticker tape, we can also see if an object was moving with constant

velocity or accelerating

o A constant distance between dots represents ____________________, or no acceleration

o A changing distance between dots indicates changing velocity, also known as

____________________________________

- We can also use “strobe pictures” in order to show velocity and acceleration in the same way

A camera take a picture of an object in motion at regular intervals

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- Vector diagrams can be used to show direction and

magnitude with a vector arrow

In a vector diagram, the size of the vector arrow tells us the ______________________________

o If all of the arrows are the same length, then the magnitude is __________________________

o In the case of a moving car, this would mean that the velocity of the car is constant while it

is moving

o If the size of the arrows increase or decrease, this would mean that the car is changing

velocity, or accelerating