Chapter 3Chapter 3

Linear Motion

1. MOTION IS RELATIVE1. MOTION IS RELATIVE

Everything moves, at least with respect to some reference point.

To describe motion we shall talk about

Speed

Velocity

Acceleration

= distance/timeUnits - m/s, ft/s, etc.

Instantaneous Speed is the speed you would

read from a speedometer.

2. Speed2. Speed

Average Speed

Example of Average SpeedExample of Average Speed

You take a trip from A to B and back to A. You want to average 60 mph for the

round trip A to B to A.

A B2 miles

From A to B you average 30 mph.

What is your average speed on the return trip from B to A?

30 mph

?

Example of Average SpeedExample of Average Speed

A B2 miles

30 mph

? 60 mi/hr is 60 mi/(60 min) or 1 mi/min. To average 1 mi/min for a 4 mi trip would

require4 min.

30 mi/hr is 30 mi/(60 min) or 1 mi/(2 min). A 2 mi trip would take 4 min. See a problem???

Sorry, Ma’am, but youwere doing 45 mph in a30 mph zone.

But I haven’t driven 45miles yet.

Speeding Little Old Lady

Okay, okay, would you believe that I haven’t been driving for an hour yet?

3. Velocity3. Velocity

Average Velocity = Displacement/time

Units - m/s, ft/s, etc.

Instantaneous Velocity of an object is its instantaneous speed plus the direction it is traveling.

Velocity is a vector.

Displacement and Average VelocityDisplacement and Average Velocity

D

tD

v

Distance traveled is the length of the path taken.

ntDisplacemeD

Average velocity =

Acceleration = "change" in velocity/time

Units – (m/s2),

4. Acceleration4. Acceleration

ss

m

ss

ft(ft/s2), etc.

Acceleration is also a vector.

Motion at constant velocity

Accelerated motion

Here Here, too

Demo - Ball on incline and ball on tableDemo - Ball on incline and ball on table

We can sense acceleration by comparing

observations from a constant velocity frame of

reference to observations from an

accelerating frame of reference.

Interpretation - we can feel acceleration if

there is a “support” force or contact.

Acceleration on Galileo's

Inclined Planes

Velocity and Acceleration

Galileo used inclined planes to study accelerations.

He found constant accelerations for inclines: the steeper the incline, the greater the acceleration. (It was too hard to measure time for free-falls.)

He also found that the size of the objects didn't matter.

Relationships Between v and a for Linear Motion.Relationships Between v and a for Linear Motion.

t

vva 0

atvv 0

atvv 0

atvIf initial velocity is zero, then

ExampleExample

A jogger starts at zero velocity with an acceleration of 3 ft/s2. How fast is she moving after 4 seconds? (Let’s see if we can first do this without using any equations.)

0v0 atv2s/ft3a

s4t )s4(s/ft3v 2

s/ft12v

Chapter 3 Review Questions

Chapter 3 Review Questions

What is the average speed of a horse that gallops a round-trip distance of 15 km in a time of 30 min?

What is the average speed of a horse that gallops a round-trip distance of 15 km in a time of 30 min?(a) 0(b) 0.5 km/h(c) 30 km/h(d) 500 m/s(e) None of the above

What is the average velocity for the round-trip of the horse in the previous question?

What is the average velocity for the round-trip of the horse in the previous question?(a) 0(b) 0.5 km/h(c) 30 km/h(d) 500 m/s(e) None of the above

5. FREE FALL

Motion near the surface of the earth in the absence of

air resistance.

The acceleration of an object is

g = 32 ft/s2 = 9.8 m/s2.

Velocity in gravitational field:

v = gt = 32t

How FastHow Fast

How FarHow Far

BC and how deep is a well.Michael Jordan – 3 s hang time??

tvd

tvd2

tgt

d2

22

2

1 tgtd 16

(If initial velocity is zero)

Free FallFree FallTime of Fall

(s)Velocity Acquired

(ft/s)Distance Fallen

(ft)

1

2

3

4

5

32

64

96

160

128

400

256

144

64

16

Demonstrations

Demo - Coin and feather in Demo - Coin and feather in vacuumvacuum

Film - Galileo's Experiment on the Film - Galileo's Experiment on the MoonMoon

Demo - Reaction timerDemo - Reaction timer Demo - Paper and book dropDemo - Paper and book drop

What is the acceleration of an object at top of its flight?

g, you should know this one.

Free Fall - How Quickly How Fast Changes

Free Fall - How Quickly How Fast Changes

Acceleration Is How Quickly How Fast Changes.

Acceleration is difficult to understand because it is a rate of a rate.

What is a rate of a rate of a rate? JERK

Chapter 3 Review Question

Chapter 3 Review Question

You throw a stone downward. It leaves your hand with a speed of 10 ft/s. What is its speed two seconds after leaving your hand? (Neglect air resistance.)

You throw a stone downward. It leaves your hand with a speed of 10 ft/s. What is its speed two seconds after leaving your hand? (Neglect air resistance.)

(a) 10 ft/s(b) 32 ft/s(c) 42 ft/s(d) 64 ft/s(e) 74 ft/s

An object dropped from rest in free fall will fall feet in the first second and feet in the second second.

An object dropped from rest in free fall will fall feet in the first second and feet in the second second.

(a) 16, 48(b) 16, 32(c) 32, 32(d) 32, 64(e) 32, 48