Phys 1111

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Phys 1111

• Chapter 2
• Motion in One Dimension

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Vectors and Scalars

• Scalars are quantities which are fully described
  by a magnitude alone.
• distance, speed, mass, volume,
• Vectors are quantities which are fully described
  by both a magnitude and a direction.
• displacement, velocity, force,

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Distance and Displacement

• Distance
• is the actual path length of a journey between
  two points
• is a scalar quantity
• meter (m) is its SI unit

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Distance and Displacement

• Displacement
• -is a a vector that points from an objects
  initial position to its final position
• -has a magnitude equal to the shortest distance
  between the two positions
• -meter (m) is its SI unit

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Distance and Displacement

• distance length of curved line
• displacement the length and direction of
  the straight line

A
B
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Distance and Displacement

• If an object moves from position x1 to x2 on a
  straight line along the x-axis
• displacement ?x x2 - x1
• distance ?x x2 - x1
• Note that
• -displacement which is a vector quantity can be
  positive or negative
• -distance Which is scalar is always positive

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Distance and Displacement

• Example1. Find the displacement and distance
  moved by the car in the figure as it moves
• From position 20km to position -10km
• From position -15km to position 20km and back
  position 5km

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Speed and Velocity
Speed is a scalar quantity which refers to "how
fast an object is moving."
The SI unit of speed is meter per second
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Speed and Velocity
Velocity is a vector quantity which refers to
"the rate at which an object changes its
position."
The SI unit of speed is meter per second
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Speed and Velocity

• Example2. Particle P moves from A to E along the
  following path in 20s time interval
• a) What distance does the particle travels
  between A and E?
• b) What is the particles displacement between A
  and E?
• c) What is the particles average velocity between
  A and E?
• d) What is the particles average speed between A
  and E?
• e) What is the particles average velocity between
  B and D?
• f) Assuming constant speed throughout the path,
  what is the particles average speed between B and
  D?

A
B
E
C
D
20m
40m
0m
10m
60m
-10m
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Speed and Velocity

• Instantaneous Speed - speed at any given instant
  in time.
• Average Speed - average of all instantaneous
  speeds found simply by a distance/time ratio.

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Speed and Velocity

• Instantaneous velocity - Velocity at any given
  instant in time.
• The velocity at any instant is obtained from the
  average velocity by shrinking the average time
  interval ?t closer and closer to 0.

Instantaneous velocity
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Speed and Velocity

• Suppose at t1 0 x1 xo and at t2 t, x2 x
• Solving for x gives us

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Speed and Velocity

• Uniform motion
• When the objects velocity is uniform (the same
  at every instant during the time interval
  analyzed)
• average velocity instantaneous velocity
• then

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Position time graph for a uniform motion
X2
?X X2 X1
X1
?t t2 t1
(0, Xo)
t1
t2
the initial position (Xo) is the vertical
intercept
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• Velocity time graph of uniform motion

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• Example3. The following figure shows the
  position-time graphs of three cars. Find the
  initial position and the average velocity of each
  car.

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• Example4. The position time graph for a motorist
  is shown in the figure below.
• Find the velocity of the motorist for the
  following time intervals i) 0-6min, ii) 6min
  12min, iii) 12min 14min, iv) 14min-16min.
• What is the average velocity of the motorist?
• What is the average speed of the motorist?
• Find the average velocity and average speed of
  the motorist for the time interval 6-15min.
• What are the instantaneous velocities of the
  motorist at i) t 1min ii) t 7.5min iii) t
  11min?

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Acceleration

• When an objects velocity change over time, the
  object is said to undergo acceleration (or to
  accelerate).
• Acceleration is defined as the rate at which
  velocity changes with time.
• If an objects velocity is v1 at instant t1 and
  v2 at instate t2 then,
• Acceleration is a vector quantity
• The SI unit of acceleration is meter per second
  per second

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Acceleration

• For object moving to the right and speeding up
• ?t value
• v2 gt v1
• v2 gt v1
• ?v value
• a value
• For object moving to the right but slowing down
• ?t value
• v2 lt v1
• v2 lt v1
• ?v -value
• a -value

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Acceleration

• For object moving to the left and speeding up
• ?t value
• v2 lt v1
• v2 gt v1
• ?v -value
• a -value
• For object moving to the left but slowing down
• ?t value
• v2 gt v1
• v2 lt v1
• ?v value
• a value

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V versus t graph
v2

?v v2 v1
v1
?t t2 t1
(0, vo)
t1
t2
the initial position (vo) is the vertical
intercept
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Instantaneous acceleration
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Constant Acceleration and Equations of Motion

• If an objects acceleration is constant, or
  uniform, the instantaneous and average
  accelerations are the same.
• For motion with constant acceleration
• If we let vo the velocity at t 0, and v the
  velocity at later instant t and solve the
  resulting equation for v, we get

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Constant Acceleration and Equations of Motion

• If an object accelerates uniformly from a
  velocity vo at time t0 to a velocity v at some
  later time t, the average velocity of the object
  is given by

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Constant Acceleration and Equations of Motion

• Using equations
• We can get

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Constant Acceleration and Equations of Motion

• x versus t graph
• (a positive)

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Constant Acceleration and Equations of Motion
x versus t graph (a negative)
(0, X0)
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Constant Acceleration and Equations of Motion

• Using and
  
• in
  
• We get

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Summary of equations of motion
uniform motion (velocity constant )
Acceleration constant
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• Example 5. The velocity of a uniformly
  accelerated body increases from 8m/s at 2s to
  14m/s at 4s.
• a) Find the bodys acceleration.
• b) Find the bodys initial velocity.
• c) Suppose the body was at x0 80m initially.
  What is the bodys position and displacement at t
  10s?

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• Example 6. A certain vehicle requires a distance
  of 30m to stop when it is traveling at 25m/s.
• a) What acceleration is produced by breaking
  under these conditions?
• b) If a jaywalker is 28m in front of the vehicle
  when the driver first applies the brakes, how
  much time does the pedestrian have to get out of
  the way?

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Gravitational Acceleration and Free Fall

• Free fall motion
• Free fall motion is the motion of an object only
  under the influence of gravity.
• Free fall motion Is an example of motion with
  constant acceleration called gravitational
  acceleration g.
• The acceleration of a freely falling object is
  independent of the objects characteristics such
  as mass, density, or shape. (In free fall all
  objects have the same acceleration).
• The gravitational acceleration g 9.8m/s2 near
  the surface of the Earth.
• g is always directed down towards the center of
  the earth.

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Equations for Free Fall

• Using a -g (upward positive) and replacing x
  by y in the Kinematic equations

position (y)
(0, Y0)
time (t)
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• Example 7. A ball is thrown straight up, with an
  initial velocity of 20m/s.
• a) Find out how long it takes the ball to reach
  its highest point.
• b) Find how high the ball goes.

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• Example 8. A stone is thrown upward with an
  initial velocity of 39.2m/s from the edge of a
  building. It just misses the edge of the building
  on the way down.
• Find the position and velocity of the stone at
  t 2.0s, 5.0s, and 10s.
• If the building is 60m high, with what speed and
  at what time does the stone hit the ground.

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Exercises

• 2.11, 2.12, 2.17, 2.22, 2.32, 2.35, 2.37, 2.40,
• 2.41, 2.47, 2.67, 2.79, 2.84, 2.89, 2.90