kinematics 1-d motion
DESCRIPTION
Kinematics 1-D Motion. Vocabulary of Motion. Distance Scalar quantity Displacement Vector quantity, Object’s change in position. 5 km. Distance traveled = 15 km Displacement = 5 km, East. 5 km. 5 km. Vocabulary of Motion. Speed Scalar Quantity - Change in distance over time. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/1.jpg)
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Kinematics 1-D Motion
![Page 3: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/3.jpg)
Vocabulary of Motion
• Distance–Scalar quantity
• Displacement–Vector quantity, Object’s
change in position
![Page 4: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/4.jpg)
• Distance traveled = 15 km• Displacement = 5 km, East
5 km
5 km
5 km
![Page 5: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/5.jpg)
Vocabulary of Motion
• Speed–Scalar Quantity- Change in distance over time
![Page 6: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/6.jpg)
Vocabulary of Motion
• Velocity–Vector Quantity
– Average Velocity =
v = Change in Position = Δd
Change in Time Δt
![Page 7: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/7.jpg)
Vocabulary of Motion
• Acceleration–Vector Quantity
a = Change in Velocity = Δv
Change in Time Δt
- Positive a – speeding up
- Negative a – slowing down
![Page 8: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/8.jpg)
Motion Graphs
• Position Vs. Time
Pos
ition
TimeObject is
Stopped, v = 0
Pos
ition
Timev = + constant
![Page 9: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/9.jpg)
• Position Vs. Time
Pos
ition
Time
v = - constant
![Page 10: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/10.jpg)
• (Not constant velocity)P
ositi
on
Time
Object is decreasing speed
over time
Pos
ition
Time
![Page 11: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/11.jpg)
Pos
ition
Time
Object is increasing speed
over timeP
ositi
on
TimeWalks away. Stops, walks back towards
start and keeps going past 0, -.
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Pos
ition
Time
Constant speed, slowing down to a stop, then
increasing speed
![Page 13: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/13.jpg)
Slope?
• The slope of a Position vs. Time graph is the objects Velocity!
Slope = Δy = Δd = v
Δx = Δt
![Page 14: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/14.jpg)
Which graph best represents the motion of a block accelerating uniformly
down an inclined plane?
![Page 15: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/15.jpg)
Motion Graphs
• Velocity vs. Time
Time
Vel
ocity
Velocity is constantTime
Vel
ocity
Increasing at a constant rate, +
![Page 16: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/16.jpg)
Time
Vel
ocity
Velocity is decreasing at a constant rate, -
Time
Vel
ocity
Velocity is decreasing, stops and
increases in the other direction
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Slope?
• The slope of a velocity vs. Time graph is its acceleration!
Slope = Δy = Δv = a
Δx = Δt
![Page 18: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/18.jpg)
Mathematical Analysis
• Finding Average Velocity
v = vi + vf or Δd
2 Δt
Note: vi = Initial Velocity
vf = Final Velocity
![Page 19: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/19.jpg)
• Acceleration
a = Δv or vf – vi
Δt Δt
![Page 20: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/20.jpg)
Problems
• A car travels 650 m in 5.0 sec. What is its average velocity??
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Problems• A car starting at rest accelerates at
2.0 m/s2 for 2.0 sec. What is its final velocity?
• A car is traveling at 35 m/s. It then accelerates at a rate of 6.0 m/s2 for 10 sec. Find the final velocity of the car.
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• Area Under Velocity vs. Time graph is the distance traveled
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Additional Motion Equations
• d = vit + 1/2at2
• vf2 = vi
2 + 2ad
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On Your Own
• A car is traveling at 35 m/s. It then accelerates at a rate of 6.0 m/s2 for 10 sec. Find the final velocity of the car.
![Page 25: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/25.jpg)
FREE FALLING!
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Free Fall
• All bodies fall at the same rate of acceleration
• The acceleration due to gravity near the Earth’s surface is 9.81 m/s2
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What does that mean?
• Every second an object falls, its speed is increasing by 9.81 m/s
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t = 0 sec, v = 0 m/s
t = 1 sec, v = 9.81 (10) m/s
t = 2 sec, v = 19.62 (20) m/s
t = 3 sec, v = 29.43 (30) m/s
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Motion GraphsP
ositi
on
Time TimeV
eloc
ity
![Page 30: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/30.jpg)
Mathematical Analysis of Free Fall
• a = g = 9.81 m/s2
• For an object being dropped, The initial velocity is ZERO.
• Motion in the y-direction (vertical)
![Page 31: Kinematics 1-D Motion](https://reader033.vdocuments.net/reader033/viewer/2022061414/56815003550346895dbdcedd/html5/thumbnails/31.jpg)
Problem . . .
• A 100 kg object is dropped from 10 m. How long does it take to hit?
• What is the final speed right before it hits the ground?