Chapter 2:Linear Motion

Conceptual PhysicsHewitt, 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

2.2 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)

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

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

2.4 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

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

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!

2.6 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)

2.7 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 dataCan 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?

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?

Figure 2.10

0 1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

400

450

d vs t

Time (s)

Dis

tance (

m)

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!

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

Ch 2 Equations & Constants

Time interval Dt = tf – ti

Displacement Dd = df – di

Velocity v = Dd/DtAcceleration ā = Dv/DtAccelerated 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)