UNIT 1 Motion Graphs

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UNIT 1Motion Graphs
Days 1 - 2
Lyzinski Physics
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- Mechanics
PHYSICS
KINEMATICS
A description of motion
- Electricity
DYNAMICS
- Magnetism
A study of what causes motion
- Optics
- Waves
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Day 1 Distance Speed Unit
Conversions Scalars d-t graphs
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Definition

• Distance (d) the length of the path
• followed by an
  object.
• If an objects path is straight, the distance
  is the length of
• the straight line between start and finish.
• If an objects path is NOT straight, the
  distance is the
• length of the path if you were to straighten
  it out and
• measure it the way you would measure the
  length of a
• curved shoelace.

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B
C
Using the number line above, what would be the
distance travelled if an object travelled from ..
1m
- A to B - A to C - A to C and then back to
A - C to B, passing through A
4m
4m 4m 8m
4m 1m 5m
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Sally and Timmy are at point A. Sally walks
directly to point C (taking the shortest path).
Timmy also takes a shortest path, but has to
stop at point B for lunch first. How much
further has Timmy walked when he arrives?
4 yd
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Definition

• Average Speed (s) the distance
• travelled during a time interval divided
  
• by the elapsed time.
• s d/Dt
• (or sd/t)

we often abbreviate Dt as t
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B
C
Larry walks from point B to point C, and then
goes directly to point A. If he walks at an
average speed of 6 mph, how long does the trip
take him?
d 3mi 4mi 7mi s 6 mi/h s d/t ? t
d/s (7mi)/(6mi/h)1.17h
1 h, 10 min
Use appropriate units
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B
C
Larry runs from point A to point B in 5 minutes
and then proceeds to jog directly to point C,
taking his time in 30 additional minutes. Find

1. Larrys average speed during the first portion of
   the trip.
2. The average speed during the second portion of
   the trip.
3. Larrys average speed for the entire trip.

s d/t (1km)/(5min) 0.2 km/min 12 km/h
s d/t (3km)/(30min) 0.1 km/min 6 km/h
s d/t (4km)/(35min) 0.114 km/min 6.86
km/h
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Unit Conversions

• Convert 5 km/h to m/s.
• Convert 60 ft/s to mi/h.
• Convert 30 mi/h to m/min!!!!

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Definition

• Scalar a quantity that has a magnitude
• only, no direction.
• YES, scalars can have units.
• What scalars have we learned about thus
  far?
• ___________ ____________
  ___________

speed
time
distance
I thought time could march backward?
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d-t graphs
At rest
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SLOPE
Speed on a d-t graph can be found by taking the
_______________.
sAB rise/run (30-0m) / (10-0s) 3 m/s
sCD rise/run (100-50m) / (20-15s) 10 m/s
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Open to in your Unit 1 packet
d-t graphs CANNOT have sharp points
NOTHING CAN STOP INSTANTANEOUSLY!!
minutes
520 170yd 350 yd (approximately)
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Day 2 Position Displacement Average
Velocity Vectors x-t graphs
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Definition

• Position (x) the location of an object with
  
• respect to a specified reference
  point.
• We choose this reference point to be the
  origin of a
• coordinate system.

6 7 8 9 10
The position of particle A is either x -3 or
x 6, depending on which reference point (or
origin) you use.
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Definition

• Displacement (Dx) the change in an
• objects position during a time
  interval.
• Dx x2 x1
• or
• Dx xf xi
• Displacement must have both a magnitude
  (size) and a
• direction (right, left, up, down, north,
  south, etc).

These are all VECTORS. Whats a vector?
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B
C
Using the number line above, find the distance
travelled and the displacement in moving from
1m, 1m right
- A to B - C to A - A to C and then back to
A - C to B, passing through A
Dx 1 (1m) 0m
4m, 4m left
8m, 0m
4m, 3m left
Dx (-2) (1m) -3m OR 3m left
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Definition

• Average Velocity ( v ) the displacement
• of an object divided by the elapsed time.
• v Dx/Dt
• (or vDx/t)

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Sam runs the 400m dash. He starts and finishes
at point A, travelling one complete circuit
around the track. Each section of the track is
100m long. His average speed during each
interval are as follows. AB 7 m/s BC 8
m/s CD 6 m/s DA 7.5 m/s
Find Sams avg. speed and avg. velocity for the
entire trip.
s d/t ? t d/s 100m/7sec 14.286
sec 100m/8sec 12.5 sec 100m/6sec 16.667
sec 100m/7.5sec 13.333 sec s d/t
(400m)/(56.786s) 7.04 m/sec
Avg Velocity 0 since Dx 0 for the entire trip.
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HONORS ONLY!!!
Sam runs the 400m dash. He starts and finishes
at point A, travelling one complete circuit
around the track. Each section of the track is
100m long. His average speeds during each
interval are as follows. AB 7 m/s, 14.286
sec BC 8 m/s, 12.5 sec CD 6 m/s, 16.667
sec DA 7.5 m/s, 13.333 sec
31.831 m

• Find Sams average speed and average velocity for
  the 1st half of the race.

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Definition

• Vector a quantity that has both magnitude AND a
  direction oh yeh!
• YES, vectors can have units.
• What vectors have we learned about thus far?
• ____________ ________________
  ___________

position
velocity
displacement
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• Scalars vs. Vectors

Displacement
has magnitude direction (example 15 cm east)
Distance
has a magnitude only (example 6 ft)
Displacement is NEVER greater than distance
traveled!
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• Scalars vs. Vectors (continued)

has magnitude direction (example 15 mi/h
North)
Velocity
Speed
has a magnitude only (example 30 km/h)
Total time for the trip from 1 to 2 2 hr
Speed d/t 15.5 km/h
Velocity Dx/t 12.5 km/h
If an object STARTS STOPS at the same point,
the velocity is ZERO! (since the displacement is
zero)
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• x-t graphs

Constant speed (Constant velocity, or constant
velocity in the direction)
Slow down, speed up, slow down,
speed up
2 moments where the object is at rest (for a
moment)
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How to get the position (x) at a certain time (t)
off an x-t graph
Example What is the position at t 30
seconds?
Go over to t 30.
Find the pt on the curve.
Find the x value for this time.
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How to calculate the displacement between two
times on an x-t graph
Example What is the displacement from t
10 to t 40?
Find x1
Find x2
Use D x x2 - x1 7 m
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How to find the distance traveled between two
times on an x-t graph.
Example What is the distance traveled from t
10 to t 40?
Find the distance traveled in the direction.
Find the distance traveled in the - direction.
Add them together. (27 m)
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Understand the difference between velocity and
speed on an x-t graph.
Example What is the average speed from t
10 to t 40 seconds?
dist10-40 27 m (previous
slide)
Avg. Speed dist/ Dt 27m /
30 sec 0.9 m/s
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Understand the difference between velocity and
speed on an x-t graph.
Example What is the average velocity from t
10 to t 40 seconds?
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Will avg. velocity EVER be greater than avg.
speed?

• NO!!!

Will avg. velocity EVER be equal to avg. speed?
YES!!! When the path travelled was one-way, in a
straight line.
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Negative Average Velocity?
Example What is the average velocity from t
20 to t 40 seconds?
Since the objects displacement is in the NEGATIVE
direction, so is its average velocity.
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Open to in your Unit 1 packet
-10 m
2) 3) 4)
avg velocity slope -15m / 6sec -2.5 m/s
s v 2.5 m/s
At rest at t 0 and t 12 sec
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5) 6)
Speeding up, const negative vel, slowing down,
speeding up, const positive velocity(slow),
speeding up, constant positive velocity (fast)
Dx x2 x1 (-10m) (10m) -20m
(approximately)