Motion in One Dimension

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Motion in One Dimension

• Chapter 2

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Speed
Mr. Wolf drives his car on a long trip to a
physics store.
Given the distance and time data for his trip,
plot a graph of his distance versus time.
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Graphing Distance Vs. Time
Slope 64 mph
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Kinematics

• Kinematics - using mathematics to describe how
  objects are moving

• One Dimensional - Rectilinear motion, moving in
  a straight line path, no rotation

examples (Vertical) Falling brick, (Horizontal)
Moving Truck on a flat road or a flat ramp
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Reference Point

• A zero location used to determine position.
  Sometimes called the origin.

Position - x
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Displacement

• Definition of Displacement
• the shortest distance between the two positions.
• Unit meter (m)
• Represented as ?x

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Position and Displacement
Initial Position-
The location where the physics problem starts
Xi
?x xf - xi
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Displacement vs. Distance

• Displacement is the shortest distance between
  start and finish.
• Distance is the total path length taken to arrive
  at point B from point A.

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Displacement vs. Distance cont.
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Speed vs. Velocity

• The Sears Tower in Chicago is 443 m tall. Joe
  wants to set the worlds stair climbing record
  and runs all the way to the roof of the tower. If
  Joes average upward speed is 0.60 m/s, how long
  will it take Joe to climb from street level to
  the roof of the Sears Tower?

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Distance 443 m Speed 0.60 m/s
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Speed vs. Velocity cont.
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Now Joe climbs to the roof of the Sears and then
back down in 1,476 sec. What is his.. a) average
speed? b) average velocity?
Xi 0
Xf 0
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• The peregrine falcon is the fastest of flying
  birds (and, as a matter of fact, is the fastest
  living creature). A falcon can fly 1.73 km
  downward in 25 s. What is the average velocity of
  a peregrine falcon?

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Instantaneous Velocity

• Instantaneous velocity is how fast the car is
  moving and the direction it is moving at any
  instant during the motion.

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Frame of Reference

• The object or position from which movement is
  determined.

• The most common frame of reference is.

the earth.
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Position-Time Graphs
Lets plot the position and time for Joe Driver.

• Note that every second, the position increases by
  25 m.

• What is the average velocity?

• Is the velocity constant?

• What is the slope of the line?

The slope of position-time graph the velocity
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Acceleration

• Acceleration is when an object changes its
  velocity over a certain time.
• Average acceleration
• Average acceleration points in the same direction
  as the change of velocity.

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Velocity-Time Graphs
Lets plot the velocity and time for Joe Driver.
The velocity is constant in this case. Since it
is not changing (DV 0), the acceleration
zero.
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Velocity-Time Graphs
What if Joe Driver increases his velocity?
The velocity is changing. The acceleration can
be determined from the slope of the velocity-time
graph.
During the 1st second, the velocity increases
from 0 to 10 m/s, during the next second it
increases another 10 m/s to 20 m/s, and so on.
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Example

• A drag racer crosses the finish line, and the
  driver deploys a parachute and applies the brakes
  to slow down. The driver begins slowing down
  when ti9.0 s and the cars velocity is vi28
  m/s. When t 12 s the velocity of the car is v
  13 m/s. What is the average acceleration?