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Chapter 3:
LINEAR MOTION
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Motion Is RelativeMotion 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.
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Speed
• Defined as the distance covered per amount of travel time (meters per second).
• In equation form:distance
Speed = time
Example: A girl runs 4 meters in 2 sec. Her speed is 2 m/s.
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Average Speed• The entire distance covered divided by the total
travel time– Doesn’t indicate various instantaneous speeds along
the way.
• In equation form:
total distance covered
Average speed time interval
Example: Drive a distance of 200 km in 2 h and your average speed is 100 km/h.
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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.
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Velocity• A description of
– the instantaneous speed of the object– what direction the object is moving
• Velocity is a vector quantity. It has– magnitude: instantaneous speed– direction: direction of object’s motion– Average velocity = (initial vel + final vel )/ 2
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Speed and Velocity
• Constant speedspeed is steady speed, neither speeding up nor slowing down.
• Constant velocityvelocity is– constant speed and – constant direction (straight-line path with no
acceleration).
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Acceleration
Formulated by Galileo based on his experiments with inclined planes.
Rate at which velocity changes over time
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AccelerationInvolves a
• change in speed, or
• change in direction, or
• both.
Example: Car making a turn
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AccelerationIn equation form:
change in velocity
Acceleration time interval
Unit of acceleration is m/s2.
or
Final velocity – Initial velocity= Acceleration x time
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An automobile is accelerating when it isA. slowing down to a stop.
B. rounding a curve at a steady speed.
C. Both of the above.
D. Neither of the above.
AccelerationCHECK YOUR NEIGHBOR
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An automobile is accelerating when it isA. slowing down to a stop. B. rounding a curve at a steady speed.C. Both of the above.D. Neither of the above.
AccelerationCHECK YOUR ANSWER
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.
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Kinematic equations of motion:
• Vf = V0 +at
• Vf2 = V0
2 + 2aD
• D = V0t+0.5at2
• Note: – valid only if acceleration is constant.– If the object is in free fall; acceleration = g = 9.8 m/s2
– Note: The above equations will be provided during the test.
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Free Fall
Falling under the influence of gravity only - with no air resistance
• Freely falling objects on Earth accelerate at the rate of 9.8 m/s2.
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Free Fall—How Fast?The velocity acquired by an object starting from rest is
So, under free fall, when acceleration is 10 m/s2, the speed is
• 10 m/s after 1 s.
• 20 m/s after 2 s.
• 30 m/s after 3 s.
And so on.
Velocity acceleration x time
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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.
Distance (1/2) x acceleration x time x time
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• The following are short problems which should give you ample exercise to get comfortable with problem solving. Also you can use these as a study guide for the test.
• Problem solving book: 10c, 11b, 16b & c, 24b &c, 26b &c. We will try to solve these (as many as possible) in class.
• If you are comfortable with the above, try the following at home: 38, 39, 42, 43, 45, 46, 51,55.(Most of these problems are very similar.)
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• Conceptual Physics textbook:
• Pg 46 – 7, 8, 10
• Pg 47 – 18, 21, 23
• Pg 49 – 5, 8, 17, 20, 27, 38, 40