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Chapter 2: Linear Motion

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

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  1. Chapter 2:Linear Motion Conceptual Physics Hewitt, 1999

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. Figure 2.10

  13. 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

  14. 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

  15. 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

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