1. Chapter 3
Linear Motion
MFMcGraw
Revised 1/25/2010

2. Linear Motion Motion is Relative Speed Instantaneous Speed
Average Speed
Velocity
Constant Velocity
Changing Velocity
Acceleration
Acceleration on Galileo’s Inclined Planes
Free Fall
How Fast
How Far
How Quickly “How Fast” Changes
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3. This lecture will help you understand:
Motion Is Relative
Speed : Average and Instantaneous
Velocity
Acceleration
Free Fall
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4. Motion Is Relative
Motion of objects is always described as relative to something else. For example:
You walk on the road relative to Earth, but Earth is moving relative to the Sun.
So your motion relative to the Sun is different from your motion relative to Earth.
MFMcGraw
Revised 1/25/2010

5. Speed Galileo is believed to be the first person to measure speed
For most situations we will be using meters / second and not spend a lot of time with the conversion of units.
100 mi/h = 160 km/h = 44 m/s
Distance is always measured relative to something.
This makes speeds relative
Examples:
Speed relative to the road
Speed of the earth relative to the sun.
Instantaneous Speed
Average Speed
distance
Speed =
time
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Revised 1/25/2010

6. Average Speed CHECK YOUR NEIGHBOR
The average speed of driving 30 km in 1 hour is the same as the average speed of driving
30 km in 1/2 hour.
30 km in 2 hours.
60 km in 1/2 hour.
60 km in 2 hours.
MFMcGraw
Revised 1/25/2010 6

7. Average Speed CHECK YOUR ANSWER
The average speed of driving 30 km in 1 hour is the same as the average speed of driving
30 km in 1/2 hour.
30 km in 2 hours.
60 km in 1/2 hour.
60 km in 2 hours.
Explanation:
Average speed = total distance / time
So, average speed = 30 km / 1 h = 30 km/h.
Same
Now, if we drive 60 km in 2 hours:
Average speed = 60 km / 2 h = 30 km/h
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Revised 1/25/2010 7

8. In what order do the balls arrive?
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9. Answers L1
Ans: C, B, A
Until the balls reach line L1 their conditions are identical. Each ball travels approximately the same distance. The ball with the largest average velocity will arrive first.
When a ball drops to a lower level its speed increases. Balls B and C both drop the same vertical distance but C spend more time at this higher velocity and therefore has the higher aveage velocity.
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10. Rank the final velocities
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11. Answers
Ans: B, A=C
Until the balls reach line L1 their velocities are equal.
When a ball drops to a lower level its speed increases. When it rises its velocity slows down. L1
Ball A remains at a constant speed.
Ball C increases its speed and then reduces it back to the same value as Ball A.
Ball B increase its velocity and stays at that value through the end of the race.
MFMcGraw
Revised 1/25/2010

12. Instantaneous Speed Instantaneous speed is the speed at any instant.
Example:
When you ride in your car, you may speed up and slow down.
Your instantaneous speed is given by your speedometer.
MFMcGraw
Revised 1/25/2010

13. Speed and Velocity
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14. Acceleration
Formulated by Galileo based on his experiments with inclined planes.
Rate at which velocity changes over time
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15. Centripetal Force Centripetal Force
Magnitude of velocity (speed) is constant.
Direction of Vel. is changing
Centripetal forces are center seeking forces. They are experienced, for example, when an object travels in a circular motion.
MFMcGraw
Revised 1/25/2010

16. Acceleration In equation form:
Unit of acceleration is unit of velocity / unit of time.
Example:
You car’s speed right now is 40 km/h.
Your car’s speed 5 s later is 45 km/h.
Your car’s change in speed is 45 – 40 = 5 km/h.
Your car’s acceleration is 5 km/h/5 s = 1 km/h/s.
MFMcGraw
Revised 1/25/2010

17. Acceleration CHECK YOUR NEIGHBOR
An automobile is accelerating when it is
slowing down to a stop.
rounding a curve at a steady speed.
Both of the above.
Neither of the above.
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Revised 1/25/2010 17

18. Acceleration CHECK YOUR ANSWER
An automobile is accelerating when it is
slowing down to a stop.
rounding a curve at a steady speed.
Both of the above.
Neither of the above.
Explanation:
Change in speed (increase or decrease) is acceleration, so slowing is acceleration.
Change in direction is acceleration (even if speed stays the same), so rounding a curve is acceleration.
Acceleration occurs due to a change in either speed or direction (or both).
When a car slows down it changes its speed, so it is accelerating.
When a car rounds a curve, although its speed is steady it is accelerating because it is changing direction.
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Revised 1/25/2010 18

19. Accelerations
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20. Acceleration
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21. Acceleration a.) b.) c.) d.) Acceleration on Galileo’s Inclined Planes
In which case is the ball experincing the largest acceleration?
a.)
b.)
c.)
d.)
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22. Which has decreasing acceleration?
a.) b.) c.)
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23. Which has increasing velocity?
a.) b.) c.)
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24. Free Fall Free Fall How Fast? (Velocity) How Far? (Distance)
How Quickly “How Fast” Changes? (Accelerations)
Free fall – only the force of gravity is acting on the object
MFMcGraw
Revised 1/25/2010

25. Gravity In terms of final velocity at the end of the motion-
Launching up at 30m/s or down at –30m/s yields the same final velocity.
Of course total flight time is longer for an up launch than a down launch.
Note the symmetry
(Use g= 10 m/s2)
Note the equal time intervals.
Magnitude of the descending velocities are equal to the magnitude of the ascending velocities.
Directions of the velocities are OPPOSITE.
Same time to go up to peak height as it takes to return to the starting level.
Conservative Force of Gravity
KE to PE to KE
1/2mv2 -> mgh -> 1/2mv2
Just a little look ahead.
MFMcGraw
Revised 1/25/2010

26. Free Fall—How Far?
The distance covered by an accelerating object starting from rest is
So, under free fall, when acceleration is 10 m/s2, the distance is
5 m/s after 1 s.
20 m/s after 2 s.
45 m/s after 3 s.
And so on.
MFMcGraw
Revised 1/25/2010

27. What are their velocities after 1 second?
Remember, velocity has a magnitude and a direction.
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28. Va = 0 m/s; Va = 5 m/s; Va = -7 m/s
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29. Summary
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30. Hewitt Warning
The author has a feature called “Next Time Questions.” These are challenging and thought provoking questions but sometimes they can be frustating.
One source of this frustration comes from his habit of sometimes including effects that were previously ignored.
A second source comes from his use of examples where several forces or effects are carefully balanced and one must predict the affect of upsetting this balance.
MFMcGraw
Revised 1/25/2010

31. Extra Slides
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Revised 1/25/2010