1D Kinematics

1
1-D Kinematics

• PART 1

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Restrictions

• All motion is along a straight line only.
• We dont care WHY an object moves. In kinematics,
  we will only examine HOW it moves.
• The moving object is considered to move like a
  particle (no rolling).

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Magnitude Scalars

• The magnitude of a measurement is its size
• Ex the number of miles between Socorro and
  Albuquerque is a magnitude
• A scalar is a quantity that has only magnitude

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Vectors

• A vector has both magnitude direction
• Ex the displacement vector from Socorro to
  Albuquerque is 70 miles long and points due north
• Vectors are equal if and only if they have the
  same magnitude and the same direction
• Ex the displacement vector from Socorro to
  Albuquerque is not equal to the displacement
  vector from Albuquerque to Socorro because the
  direction of the vectors is different

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Distance vs. Displacement

• Distance is a scalar quantity (it has magnitude
  only).
• Displacement is a vector quantity and is always
  relative to the origin.

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Distance vs. Displacement

• Stand in one of tiles on the floor (leave a good
  amount of room between you and your neighbor.)
• This is your origin. Determine /- directions.
• Move 3 tiles to the right.
• Move 2 tiles forward.
• Move 5 tiles to the left.
• Move 2 tiles backward.

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Distance vs. Displacement

• What is your displacement?
• What is the total distance you traveled?
• Displacement is noted ?x.
• ?x x x0

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Scalar or Vector?

• The acceleration of a plane as it takes off?
• The number of passengers on the plane
• The duration of the flight
• The displacement of the flight
• The amount of fuel required for the flight
• The odometer reading in your car
• The speedometer reading in your car

Vector Scalar
Vector Scalar
Vector Scalar
Vector Scalar
Vector Scalar
Vector Scalar
Vector Scalar
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Speed vs. Velocity

• Average Speed
• (scalar)
• Distance Traveled
• Total time

• Average Velocity
• (vector)
• Displacement
• Total time

Velocity has a direction!!
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Try it

• Calculate the average speed and average velocity
  of a complete round-trip in which the outgoing
  200 km is covered at 90 km/h, followed by a
  one-hour lunch break, and the return 200 km is
  covered at 50 km/h.

Average speed 60 km/h Average velocity 0
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Acceleration

• Average Acceleration
• (vector)
• Velocity
• Total time

Acceleration is the rate of change of
velocity. Units m/s2
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The Kinematics Equations

• The Kinematics equations are based on two very
  important assumptions
• Constant acceleration. Many situations exhibit
  uniform (constant) acceleration. Since
  acceleration is constant, the average and
  instantaneous acceleration are equal
• t0 0. Since we can create our own reference
  system, we might as well make it an easy one.

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Kinematics Equations
No time
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Try it

• A car slows down from 25 m/s to rest in a
  distance of 85 m. What was its acceleration,
  assumed constant?

a -3.7 m/s2
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Try some more

• A light plane must reach a speed of 30.0 m/s for
  takeoff. How long a runway is needed if the
  acceleration is 3.0 m/s2?
• A car traveling at 45 km/h slows down at a
  constant 0.50 m/s2 just by letting up on the
  gas. Calculate (a) the distance the car coasts
  before it stops, (b) the time it takes to stop,
  and (c) the distance it travels during the first
  and fifth seconds.

x 1.5 x 102 m
(a) 160 m
(b) 25 s
(c) 12 m, 10 m
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Falling Objects

• When gravity acts on an object, what happens?
• The object falls
• We call this free fall
• An object is in free fall when it is affected
  only by gravity
• astronauts

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Falling Objects

• Conveniently, you can use the same kinematics
  equations with falling objects (your system is
  just vertical instead of horizontal).
• Replace position x with position y
• Is the acceleration in vertical motion constant
  or changing?
• g 9.81 m/s2

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Kinematics Equations
Horizontal Motion
Vertical Motion
No time
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Gravity

• What is the direction of gravity?
• Toward the center of the planet.
• What is the sign (/-) of gravity?
• The sign of g is often debated. The key is to
  always draw a picture, label your coordinate
  system and stick with it.
• If you call up the positive (y) direction,
  what sign does gravity have?
• What if you decide down is positive?

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Questions

• Will a Nerf ball and a softball fall at the same
  rate?
• How about a feather and a rock?
• Are acceleration and velocity always in the same
  direction?
• If you throw an object up in the air and catch it
  again, what is the velocity at the top of its
  arc? What is its acceleration?

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King Kong

• Exhausted by hours of batting away planes, King
  Kong topples off the Empire State Building.
  Calculate (a) how long it will take the big ape
  to reach the ground (assume a straight path, h
  380 m), and (b) his velocity just before
  landing.
• Draw a picture.
• Label coordinates (axis)
• List known variables
• Determine what youre looking for

(a) t 8.8 s
(b) v 86 m/s
Do we need to know King Kongs weight?
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More Good Stuff

• A stone is dropped from the top of a cliff. It is
  seen to hit the ground below after 3.50 s. How
  high is the cliff?
• A stone is thrown vertically upward with a speed
  of 20.0 m/s. (a) How fast is it moving when it
  reaches a height of 12 m? (b) How long is
  required to reach this height? (c) Why are there
  two answers to (b)?

y 60.1 m
(a) v 13 m/s
(b) t 0.73 s, 3.3 s
(c) the motion follows a parabolic path