Chapter 2: Linear Motion

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# Chapter 2: Linear Motion - PowerPoint PPT Presentation

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

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)
• 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

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

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

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

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

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

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

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

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

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

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
• 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

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