Chapter 2: Motion in One Dimension Date _______
Aristotle (384 ­ 322 BC): Motion was divided into 2 categories
1) Natural motion ­ every object had a proper place determined by its "nature"
Any object not in its proper place would strive to get there like a rock falling to the ground.
2) Violent motion ­ imposed motion
An push or pull on an object was violent motion.
He believed that heavier objects would fall faster to the ground.
Provided that an object was in its proper place, its normal state was one of rest.
Copernicus (early 1500s): His theory was that the Earth moved around the sun based on astronomical observations. This didn't make sense with the prevailing ideas of motion
Aristotle's ideas were part of the Church's doctrine so to question the ideas about motion was to question the authority of the church
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Galileo Galilei (1564 ­ 1642): discredited Aristotle's ideas of motion
He experimented by dropping objects with various weights from the top of the Leaning Tower of Pisa. He saw that except for the small effect of air resistance, objects when released at the same time, fell together and hit the ground at the same time.
He experimented with inclined planes and found that a ball going down an inclined plane picked up speed and a ball going up an inclined plane lost speed. From here he reasoned that a ball rolled on a horizontal plane would come to rest not because of its "nature" but because of friction.
He did experiments with inclined planes made of different materials and found that when there was less friction the ball rolled farther. He reasoned that in the absence of friction or other forces, a horizontally moving object would continue moving forever.
He called this property of continuing to move inertia. This concept discredited Aristotle's ideas of motion.
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One Dimensional Motion is the motion like that of a train on a straight track.
The train can only move forward or backward NOT up or down.
In order to understand simple one dimensional motion and more complicated motion like projectiles, one must chose a frame of reference.
Frame of reference is the point from which motion is determined. It is a perspective on the motion. If an object is at rest, its position does not change with respect to a fixed frame of reference.
The green car is moving with respect to
The green car is NOT moving with respect to The most common frame of reference is __________
The motion of an object depends on the frame of reference that you choose.
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Distance, d, is how much ground an object has covered. Units:
Displacement, Δx, is how far out of place an object is from its original position including direction.
Units:
The gecko's displacement is the difference between its final position and its initial position.
∆x = xf – xi displacement = final position – initial position
Displacement is not always equal
to the distance traveled.
A
B
In which picture is the distance travelled not equal to the displacement? Why?
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Since displacement includes direction, it can be positive or negative.
Unless otherwise stated we will use right, or east and positive and left or west as negative.
Also, upward or north will be positive and downward or south to be negative.
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Time, t, is the length of time something takes. Units:
Velocity, vavg, is the displacement divided by the time interval during which the displacment occurred. The SI unit of velocity is meters per second, m/s. The direction must be included.
The average velocity of an object can be
positive or negative depending on the sign
of the displacement.
What is the average velocity if you drive west 370 kilometers, km, to your friends hours in 5 hours? 6
Velocity is not the same as speed.
Velocity describes motion with both a direction and a numerical value (magnitude) that indicates how fast an object moves.
An object's average speed is equal to the distance traveled divided by the time for that motion.
Average speed = Distance traveled
Time of travel
Velocity is speed with direction.
Equations for speed Equations for average velocity
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Practice Problems
1) Nick walks with an average velocity of 0.98 m/s eastward. If it takes him 30 min (1800 sec) to walk to a store, what is his displacement?
2) If George rides his bike in a straight line for 15 min (.25 h) with an average velocity of 12.5 km/h south, how far has he ridden?
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3) A bus travels 280 km south along a straight path with an average velocity of 88 km/h south. The bus stops for 24 min (0.4 h). Then is travels 210 km south with an average velocity of 75 km/h south. How long does the trip last?
What is the average velocity for the total trip?
What is the average speed for the total trip?
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Instantaneous Velocity: The velocity of an object at any ONE instant.
Example:
Instantaneous Speed. The speed of an object at any ONE instant.
Example:
Constant Velocity: The velocity (speed and direction) of the object does not change. Example:
Constant Speed: The speed of the object does not change.
Example:
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