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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