linear motion. objectives understand the concept of relative motion. know the distinction between...
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Linear Motion
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Objectives
• Understand the concept of relative motion.• Know the distinction between distance and
displacement.• Understand the concepts of average velocity
and average speed.• Be able to solve simple velocity or speed
problems.
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Relative Motion and Time
• Is the apple moving?
• All motion is relative; it must be compared to other objects (matter and space).
• time: a 4th dimension in which events (motion) occur• Time and space are closely related: how do you
know time has passed if there is no motion?
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Displacement and Distance
• displacement: a change in position (vector)• distance: how far something travels (scalar)• We tend to say distance when we mean displacement.
A
B
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Average Velocity and Speed
• average velocity: displacement during unit of time (m/s, mph); velocity is a vector quantity (specific direction)
• average speed: total distance covered over a time interval; speed is a scalar quantity (no direction)
• What is the average speed (in mph and m/s) if it takes 4 hr 42 min to drive the 268 miles to Bozeman, including breaks? 1.00 mph = 0.447 m/s.
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Indicating Velocity
• Consider a collision between two cars, one traveling at 55 mph and the other at 57 mph. Is it a bad wreck?
• It depends on the direction!
• We represent direction using +/- signs or vectors.
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Objectives
• Understand the concept of acceleration.• Be able to solve acceleration problems using
the kinematic equations.
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Acceleration
• acceleration: a change in velocity over a time interval; vector quantity
• You can accelerate by (1) speeding up, (2) slowing down, or (3) changing direction.
• A ball is rolled up an incline at 4.6 m/s. 3.5 seconds later it is rolling down at 2.8 m/s. What is the acceleration?
t
v
t
vva if
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The Kinematic Equations
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Equations used for uniform acceleration…
t
vva if tavv if
221 tatvd i
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Kinematic Problems
• How much time does it take to accelerate from rest to 22.5 m/s at 1.5 m/s2?
• Suppose you accelerate at 2.0 m/s2 from 15 m/s to 21 m/s. How much distance is covered?
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Motion Graphs: Slope
• The slope of a graph = rise/run.• This slope represents d/t, or velocity!• A constant slope means a constant
velocity• A changing slope means a changing
velocity (an acceleration).
time
disp
lace
men
t
time
disp
lace
men
t
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Motion Graphs: Area• For a velocity vs. time
graph, the area-under-the-curve equals v · t, or displacement.
• Notice how the area (displacement) is proportional to time squared.
• Galileo discovered this!time
velocity
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Objectives
• Understand the concept of freefall.• Be able to solve freefall problems using the
kinematic equations.
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Free Fall
• Due to gravity, objects accelerate at -9.81 m/s2 (roughly -10 m/s2).
• This acceleration due to gravity is called g.
• Kinematic equations can be used to determine time (t), velocities (vi or vf) or the height (d).
GRA
VITY
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Free Fall: Velocity
• If you throw a ball upwards at +30 m/s, it will accelerate at g.
• Just keep taking -10 m/s from the velocity each second.
• When solving problems, use g = -9.81 m/s2.
+30 m/s
+20 m/s
+10 m/s0 m/s
- 10 m/s
- 20 m/s
- 30 m/s
- 40m/s
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Freefall Problems
• A ball is thrown upward at +25.2 m/s. What is its height after 3.8 seconds?
• How deep is a well if it takes 4.6 seconds for a rock to fall to the bottom?
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Proportionalities
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xy ~
directly proportional
linear graph
inversely proportional
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hyperbolic graphxy 1~
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2
21 tatvd i
2~ xy
directly proportional to the square
parabolic graph
inversely proportional to the square
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r
qqkF
2
1~x
y very steephyperbolic graph
Proportionalities