Physics 121

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Physics 121
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2. Motion in one Dimension
2.1 Reference Frames and Displacement 2.2
Average Velocity 2.3 Instantaneous Velocity 2.4
Acceleration 2.5 Motion at Constant
Acceleration 2.6 How to Solve Problems 2.7
Falling Objects 2.8 Graphs of Linear Motion
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Speed

• Speed Distance / Time
• v d / t

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Example 2.1 . . . From a Distance
If you are driving 110 km/h along a straight road
and you look to the side for 2.0 s, how far do
you travel during this inattentive period?
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Solution 2.1 . . . From a Distance
Given v 110 km/h t 2.0 s Solve
for d
Formula v d/t
But first convert speed (v) into m/s!!!
110 km/h 110 km/h x 1000 m/km / 3600 s/h
110 km/h 30.6 m/s
v d/t 30.6 m/s d / 2.0 s d 30.6 m/s x 2.0
s d 61 m
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Distance and Displacement
Displacement measures the change in position of
an object. Also, the direction, in addition to
the magnitude, must be considered. Distance
and Displacement can be very different if the
object does not proceed in the same direction in
a straight line!
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Example 2.2 . . . Around the block
A car travels East from point A to point B (5
miles) and then back (West) from point B to point
C (2 miles). (a) What distance did the car
travel? (b) What is the cars displacement?
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Solution 2.2 . . . Around the block
A car travels East from point A to point B (5
miles) and then back (West) from point B to point
C (2 miles). (a) Distance traveled is 7
miles (b) Displacement is 3 miles East
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Speed and Velocity

• Velocity displacement / time
• Car A going at 30 m.p.h. EAST and car B going at
  30 m.p.h. NORTH have the same speed but different
  velocities!
• A car going around a circular track at 30 m.p.h.
  has a CONSTANT SPEED but its VELOCITY is
  CHANGING!

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Example 2.3 . . . Speed and Velocity
John Denver negotiates his rusty (but trusty)
truck around a bend in a country road in West
Virginia. A. His speed is constant but his
velocity is changing B. His velocity is
constant but his speed is changing C. Both his
speed and velocity are changing D. His velocity
is definitely changing but his speed may or may
not be changing
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Solution 2.3 . . . Speed and Velocity
John Denver negotiates his rusty (but trusty)
truck around a bend in a country road in West
Virginia. A. His speed is constant but his
velocity is changing B. His velocity is
constant but his speed is changing C. Both his
speed and velocity are changing D. His velocity
is definitely changing but his speed may or may
not be changing
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Example 2.4 . . . On the road again!
A car travels East from point A to point B (5
miles) and then back (West) from point B to point
C (2 miles) in 15 minutes (a) What is the speed
of the car? (b) What is velocity of the car?
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Solution 2.4 . . . On the road again!
A car travels East from point A to point B (5
miles) and then back (West) from point B to point
C (2 miles). (a) Speed is 28 mph (b) Velocity
is 12 mph East
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Instantaneous Velocity

• Instantaneous means measured at a given instant
  or moment (Kodak moment). Experimentally, this
  is virtually impossible. One must measure the
  distance over an extremely short time interval
• Average means measured over an extended time
  interval. This is easier to measure.

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Speed and Velocity . . . revisited!

• Speed distance / time
• Velocity displacement / time
• For translational motion (straight line) in the
  same direction, speed equals velocity!
• Speed is an example of a SCALAR quantity. Only
  the magnitude (amount) is specified without
  regard to the direction
• Remember to specify the magnitude and the
  direction for displacement and velocity. These
  are VECTOR quantities

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Acceleration

• Acceleration is the rate of change of velocity
• a ( vf - vi ) / t

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Example 2.5 . . . Uniformly accelerating car
When the traffic light turns green, the speed of
a car increases uniformly from vi 0 m/s at t
0 s to vf 18 m/s at t 6 s (a) Calculate the
acceleration (b) Calculate the speed at t 4
s (c) Calculate the distance traveled in 6 s
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Solution 2.5 . . . Uniformly accelerating car
Vf Vi a t Vf 0 3x4 Vf at 4s 12 m/s
a (Vf - Vi ) / t a (18 - 0) / 6 a 3 m/s2
Vave (Vf Vi ) / 2 Vave (180)/2 Vave 9 m
/s
Vave d / t 9 m/s d / 6 s d 54 m
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Example 2.6 . . . Motion in one dimension

• Is the speed constant at t10s?
• When is the acceleration zero?
• When is it slowing down (decelerating)?
• What is the acceleration at t7s?

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Solution 2.6 . . . Motion in one dimension

• Is the speed constant at t10s? No
• When is the acceleration zero? 13 s lt t lt 42 s
• When is it slowing down (decelerating)? t gt 42 s
• What is the acceleration at t7s? 1 m / s2

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Equation Summary for uniform acceleration (No
Jerks Pleeeease!)

• Vave d / t
• Vf Vi a t
• Vave (Vf Vi) / 2
• d Vi t 1/2 a t2
• Vf2 Vi2 2ad

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Example 2.7 . . . Drivers not a jerk!
A car accelerates from a stop light and attains a
speed of 24 m/s after traveling a distance of 72
m. What is the acceleration of the car?
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Solution 2.7 . . . Drivers not a jerk!
Given Vi 0 Vf 24 m/s d 72 m
Solve for a
Formula Vf2 Vi2 2ad
(24)2 0 (2)(a)(72) a 4 m/s2
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Example 2.8 . . . Free Fall
Acceleration due to Earths gravity is 9.8 m/s2
(a) A cat falls off a ledge. How fast is it
moving 3 seconds after the fall? (b) What is the
distance traveled by the unfortunate cat?
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Solution 2.8 . . . Free Fall
Given Vi 0 a 9.8 m/s2 t
3 s Solve for Vf d
Formula Vf Vi a t d Vi t 1/2
a t2
Vf 0 (9.8)(3) Vf 30 m/s
d 0 (1/2)(9.8)(3)(3) d 44 m
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Example 2.9 . . . Grannys Orchard
Big apple is twice as big as Little apple. Both
fall from the same height at the same time.
Which statement is correct? A. Both reach the
ground at about the same time B. Big reaches
the ground way before Little does C. Little
reaches the ground way before Big does
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Solution 2.9 . . . Grannys Orchard
Big apple is twice as big as Little apple. Both
fall from the same height at the same time.
Which statement is correct? A. Both reach the
ground at about the same time B. Big reaches
the ground way before Little does C. Little
reaches the ground way before Big does
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Thats all folks!