Chapter 2: Motion Along a Line

1
Chapter 2 Motion Along a Line

• Position Displacement
• Speed Velocity
• Acceleration
• Describing motion in 1D
• Free Fall
• CQ 1, 2, 3, 4.
• P1, 11, 13, 25, 27, 29, 47, 50.

2
Applications

• Destination times
• Design packing materials road barriers
• Airbag deployment speed
• Simulations (movies games)

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Speed

• Speed rate of travel at a given moment of time
• Distance traveled total length of the curved
  path

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Initial/Final Notation
Same rules apply for all variables
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Delta Notation
called Displacement
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Velocity (m/s)
When Dt is small, Dx/Dt is the instantaneous
velocity v.
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Graphs

• Wilson (12) x vs t
• Giambattist (21) , -, 0 accel.
• area under v vs. t curve displacement

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Acceleration (m/s/s)
If Dt is small, Dv/Dt is called the instantaneous
acceleration and labeled a.
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Ex. Car Acceleration
0
from 10m/s to 15m/s in a time of 2.0 seconds.
In this class we only use average acceleration
and often drop the avg notation from
acceleration.
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Velocity Formula
11
acceleration

• Wilson (15) negative acceleration

12
Average Velocity with Uniform Acceleration

• Uniform Acceleration constant valued
  acceleration
• During uniform acceleration, average velocity is
  halfway between vo and v

13
Average Velocity Formula
14
Displacement Formula
15
V-squared Equation
16
Kinematic Equations with Constant Acceleration
0
17
Ex. Human Acceleration
In the 1988 Olympics, Carl Lewis reached the 20m
mark in 2.96s (Bolt 2.87s)
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Ex V2 Equation
0
Approximate Stopping Accelerations in m/s/s Dry
Road 9 (anti-lock) 7 (skidding) Wet
Road 4 (anti-lock) 2 (skidding)
At 60mph 27m/s, what is the skid-to-stop
distance on a wet road?
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Scalars Vectors

• Scalar size only
• e.g. speed, distance, time
• Vector magnitude and direction
• e.g. displacement, velocity, acceleration
• In one-dimension the direction is determined by
  the or sign.
• In two-dimensions, two numbers are required.

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Motion Diagrams
0

• Are velocity-position diagrams
• More visual than a graph of x or v vs. time
• Arrow gives direction, length represents the
  speed (use a dot for zero speed)
• (net) force required to change velocity
• Example car speeding up to left

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Free-Fall Acceleration

• a 9.8m/s/s in downward direction
• Ex. Speed of object dropped from rest after 1.0,
  2.0, 3.0 seconds
• v vo at
• v(1.0s) 0 (-9.8)(1.0) -9.8m/s
• v(2.0s) 0 (-9.8)(2.0) -19.6m/s
• v(3.0s) 0 (-9.8)(3.0) -29.4m/s
• /

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Activities

• Moving Man phet animae
• Textbook type problems

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Summary

• speed rate of travel
• average speed distance traveled/time.
• displacement change in position
• velocity rate position changes
• acceleration rate velocity changes
• kinematic equation set
• free fall constant acceleration.
• graphs and slopes