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Chapter 2: Linear Motion. Conceptual Physics Hewitt, 1999. Movement is measured in relationship to something else (usually the Earth) Speed of walking along the aisle of a flying plane Measured from the ground or from inside the plane? Time- measured in seconds (s)

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chapter 2 linear motion

Chapter 2:Linear Motion

Conceptual Physics

Hewitt, 1999

2 1 motion is relative

Movement is measured in relationship to something else (usually the Earth)

    • Speed of walking along the aisle of a flying plane
      • Measured from the ground or from inside the plane?
  • Time- measured in seconds (s)
    • Time interval- Dt = tf – ti
    • Example- 4 seconds – 2 seconds = 2 seconds
  • Displacement- measured in meters (m)
    • Dd = df – di
    • Example- 24m – 10m = 14m
2.1 Motion is Relative
2 2 speed

Speed- A measure of how fast something moves

    • Rate- a ratio of two things (second thing is always time)
    • Speed- rate of distance covered in an interval of time
      • distance/time; measured in meters/second (m/s)
      • Scalar quantity- numbers and labels only
  • In a car, measured in kilometers per hour (km/hr)
    • 62mi/h = 100 km/h = 28 m/s
  • Instantaneous speed- speed at a very brief moment of time
    • Your cars speedometer only measures instantaneous speed
  • Average speed- speed over a great amount of time
    • Average speed = (total distance covered)/(total time for trip)
2.2 Speed
speed example

If it took 25 minutes to get to school (with no stops) and school is 11.05 miles away…

    • Convert to hours- 25/60 = 0.41 hr
    • Convert to km- (11.05)(100/62) = 17.82 km
    • 17.82/0.41 = 42 km/h
    • Convert to s- (25)(60/1) = 1500 s
    • Convert to m- (11.05)(100/62)(1000) = 17820 m
    • 17820/1500 = 11.88 m/s
Speed Example
2 3 velocity

Velocity- similar to speed but is called a vector quantity

    • Same units as speed
    • Vector- magnitude (number portion) and direction
      • Speed (11.88m/s) and direction (SE)
  • Constant velocity- unchanging speed and direction
  • Changing velocity- changing either speed and/or direction
    • Speeding up, slowing down, and/or turning
2.3 Velocity
2 4 acceleration

Acceleration- another rate (based on time)

    • Rate of velocity change (m/s2) ā = Dv/Dt
    • (change in velocity)/(time interval)
    • Not just speeding up, but slowing down as well
      • Slowing down- negative acceleration
  • Calculating acceleration in a straight line can be calculated, but if the change in velocity is from turning, then it is just reported
2.4 Acceleration
acceleration example

Example: speeding up from a dead stop to 50m/s in 6 s

  • ā = Dv/Dt = (vf - vi)/(tf - ti) =
  • (50-0)/6 =
  • 8.3 m/s2
Acceleration Example
2 5 free fall how fast

Free fall- a falling object with nothing to stop it

    • Affected only by gravity (wind resistance is negligible)
    • Vertical motion
  • Acceleration- change in speed/time interval
    • For every second, objects on Earth speed up another 9.8m/s
    • See Table 2.2, page 17
  • To calculate instantaneous speed, rearrange the equation
    • v=at
    • Since we are on Earth, a=g=9.8m/s2
    • v=gt
  • g always points down, so throwing up is negative!
2.5 Free Fall: How Fast
2 6 free fall how far

Looking at Table 2.2, it’s harder to see a relationship, so we look to our formula

  • Since we usually count our starting position as our “zero” point for distance and velocity
  • d= ½(ā)(t2) (horizontal motion)
  • d= ½(g)(t2) (vertical motion)
2.6 Free Fall: How Far
2 7 graphs of motion

See Page 23, Figure 2.10

  • Position-time graphs- time is always on independent (bottom/horizontal)
  • Graph is a representation of table data
  • Can predict t or d if a best-fit line is drawn
    • Instantaneous position
    • Slope of line is velocity (d/t) (rise over run)
  • Should it be changing like that?
2.7 Graphs of Motion
more graphs

See page 23, Figure 2.9

  • Velocity-time graphs- time is always on independent (bottom/horizontal)
    • Can predict t or v if a best-fit line is drawn
    • Slope of line is acceleration (v/t)
  • Should it be constant?
More Graphs
physics in sports hang time

We just determined that d= ½(g)(t2)

    • If we rearrange the equation to solve for t, we can find the hang time of a basketball player!
  • t = √(2d/g)
    • If d=1.25m, then t = √(2x1.25/9.8) = 0.50s
  • That’s just the time going up, so double it!
Physics in Sports: Hang Time
2 8 air resistance falling objects

Although we can’t see it, air pushes back on us when we are in motion

    • Think of trying to swim very fast through water…
  • We won’t calculate it in our labs, but we need to be aware of it when thinking of error
2.8: Air Resistance & Falling Objects
ch 2 equations constants

Time interval Dt = tf – ti

    • Displacement Dd = df – di
  • Velocity v = Dd/Dt
  • Acceleration ā = Dv/Dt
  • Accelerated distance d= ½(ā)(t2)
  • Accel. Due to Gravity g = 9.80 m/s2
  • Freefall distance d= ½(g)(t2)
  • Time of freefall t = √(2d/g)
Ch 2 Equations & Constants