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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 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

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) = km 17.82/0.41 = 42 km/h Convert to s- (25)(60/1) = 1500 s Convert to m- (11.05)(100/62)(1000) = m 17820/1500 = 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 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

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 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

11 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

12 Figure 2.10

13 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

14 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

15 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

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