Motion in One DimensionMotion in One Dimension

AKA… Linear Motion

One-Dimensional MotionOne-Dimensional Motion

______________ motion takes place only in one direction.

Example: The train can move either forward or backward along the tracks. It cannot move left or right.

In another words…An object can move _______ or ________, but not ____________ and _________ at the same time.

Frame of ReferenceFrame of Reference

______________ – a system for specifying the precise location of objects in space and time

“Another words, a reference point to measure _________________.”

Example: ___________________

DistanceDistance

Is a _______ quantity Has _________, but no _________ Measures the _______ between two

objects without indicating _______ from each other

Example: _____________________

DisplacementDisplacement

A _______ quantity Has __________ and ___________

____________ – change in position of an object

Units: ___________

Displacement =

Example of DisplacementExample of Displacement Displacement is _____ always equal

to the distance traveled.

Example if you walk three steps forward, and three steps back… Your distance is ????

Your magnitude is _______!

Displacement ContinuedDisplacement Continued

Displacement can be ______ or ______ Unless otherwise stated,

Displacement to the right is ______Displacement to the left is ______Upward displacement is _______Downward displacement is _______

Examples: _______________________

Can be Pos or Neg…Can be Pos or Neg…

1. MOTION IS RELATIVE1. MOTION IS RELATIVE

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

To describe motion we shall talk about

___________

___________

___________

= ___________Units – _____________

___________ 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 = ______________

Units - _________________

Instantaneous Velocity of an object is its _____________ plus the __________ it is traveling.

Velocity is a _________.

Speed vs. VelocitySpeed vs. Velocity

Velocity is NOT the same as speed. Speed has ________ only (how fast)

Example: _______

Velocity has _______ and _______Example: ____________

**** +/- can serve as a direction

Average VelocityAverage Velocity

Units: meters per second, m/s

Average Velocity = change in position change

in time

Vavg = Δ x = xf − xi

Δ t tf − ti

Displacement and Average VelocityDisplacement and Average Velocity

D

tD

v

Distance traveled is the length of the path taken.

ntDisplacemeD

Average velocity =

Velocity can be interpreted Graphically

Velocity can be interpreted Graphically When an object’s position is

plotted versus time, the _____ of a position-time graph is the object’s velocity.

Instantaneous Velocity is NOT Average Velocity

Instantaneous Velocity is NOT Average Velocity

Instantaneous Velocity is the velocity of an object at ________________

Example: When you glance down at your speedometer while driving, the speed indicated by the speedometer is the magnitude of your instantaneous velocity. (or how fast you are going at that instant)

Acceleration = __________________

Units –

4. Acceleration4. Acceleration

Acceleration is also a ________.

Has both magnitude and direction

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 ____________ to study accelerations.

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

He also found that the size of the objects ______ matter.

Average AccelerationAverage Acceleration

Average Acceleration =

aavg =

Units: ________

Determining Acceleration Graphically

Determining Acceleration Graphically

When a graph of an object’s velocity over time is produced, the slope of the _____________ graph is the acceleration of the object.

When the velocity of an object is constant, the acceleration is _____.

Velocity and AccelerationVelocity and Acceleration

An object with a + velocity and + acceleration is __________

An object with a + velocity and - acceleration is __________

An object with a - velocity and - acceleration is __________

An object with a - velocity and + acceleration is __________

Negative ValuesNegative Values

A negative value for the acceleration of an object does not always indicate that the object is decelerating. If the object is traveling in the negative direction, a negative acceleration would result in the object moving ________ in the _______ direction.

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.)

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

Some formulas relating to displacement, velocity,

and acceleration:

Some formulas relating to displacement, velocity,

and acceleration: Finding Displacement with

Constant Uniform Acceleration∆x = ½ (Vi + Vf) ∆t

Finding Final Velocity with Constant Uniform Acceleration

Vf = Vi + a∆t

Formulas ContinuedFormulas Continued

Finding Displacement with Constant Uniform Acceleration∆x = vi∆t + ½ a (∆t)2

Finding Final Velocity after DisplacementVf

2 = Vi2 + 2a∆x

5. FREE FALLMotion near the surface of the earth in the absence of air

resistance, ______

___________________________.

The acceleration of an object is

g = __________ = _____________.

David Scott and the moonDavid Scott and the moon

David Scott demonstrated this on the moon in 1971 when he dropped a hammer and a feather at the same time. Both the hammer and the feather landed on the moon’s surface at _____________ time.

A Ball thrown upward:A Ball thrown upward:

While its velocity is positive (up), the acceleration on the ball is negative (down), so the ball ____________ as it climbs.

At the top of the balls flight, its velocity is reduced to zero, but its acceleration will still be _________ (downward).

As the ball falls, its velocity is ______ (down) and its acceleration is ______ (down), so the ball ____________.