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Physics B. Welcome to. Dr. Bertrand pbertrand@ortn.edu 425-9500 x 2568 http://moodle521.occ.utk.edu. 3-Ring Binder (with sections). Notes Homework Quizzes and Tests Lunch Bunch Notes (Physics B only) Lunch Bunch Homework (Physics B only) Lunch Bunch Quizzes and Tests (Physics B only).

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Dr. Bertrand

pbertrand@ortn.edu

425-9500 x 2568

http://moodle521.occ.utk.edu

3-Ring Binder (with sections)
• Notes
• Homework
• Quizzes and Tests
• Lunch Bunch Notes (Physics B only)
• Lunch Bunch Homework (Physics B only)
• Lunch Bunch Quizzes and Tests (Physics B only)
Kinematics

The branch of mechanics that studies the motion of a body without caring about what caused the motion.

Particle
• Has position and mass.
• Has NO size or volume.
• Located at one point in space.
Position
• Location of a particle in space.
• One dimension (x)
• Two dimensions (x,y)
• Three dimensions (x,y,z)

1-Dimensional Coordinates

x = 1 m

-1

0

1

2

3

X (m)

Distance
• The total length of the path traveled by an object.
• Does not depend upon direction.
• “How far have you walked?”

xf = -1 m

1-Dimensional Coordinates

Distance moved by particle is 2 meters.

xi = 1 m

-1

0

1

2

3

X (m)

Displacement
• The change in position of an object.
• Depends only on the initial and final positions, not on path.
• Includes direction.
• “How far are you from home?”
Displacement
• Represented by x.
• x = x2 - x1

where

x2 = final position

x1= initial position

xf = -1 m

1-Dimensional Coordinates

Distance moved by particle is 2 meters.

Displacement of particle is -2 meters.

xi = 1 m

-1

0

1

2

3

X (m)

Distance vs Displacement

B

100 m

displacement

50 m

distance

A

Average Velocity LaboratoryToday

Do lab in assigned groups.

Record results in table at front of room.

Finish lab write-up at home if necessary.

Average Speed

save = d

t

Where:

save = rate (speed)

d = distance

t = elapsed time

Average Velocity

vave = ∆x

∆t

Where:

vave = average velocity

∆x = displacement (x2-x1)

∆t = change in time(t2-t1)

Velocity vs Speed
• Average speed is always positive.
• Average velocity can be positive or negative depending direction.
• Absolute value of velocity can be used for speed if the object is not changing direction.

B

x

Dx

A

Dt

t

Average Velocity

Vave = Dx/Dt, or the slope of the line connecting A and B.

A

x

B

Dx

Dt

t

Average Velocity

Vave = Dx/Dt; still determined by the slope of the line connecting A and B.

x

t

Instantaneous Velocity

B

Determined by the slope of the tangent to a curve at a single point.

Acceleration
• A change in velocity is called acceleration.
• Acceleration can be
• speeding up
• slowing down
• turning
Uniformly Accelerated Motion
• In Physics B, we will generally assume that acceleration is constant.
• With this assumption we are free to use this equation:

a = ∆v

∆t

Units of Acceleration

The SI unit for acceleration is m/s2.

Sign of Acceleration

Acceleration can be positive or negative.

General Rule

If the sign of the velocity and the sign of the acceleration is the same, the object speeds up.

If the sign of the velocity and the sign of the acceleration are different, the object slows down.

Accelerating objects…

Note: each of these curves has many different slopes (many different velocities)!

x

t

Another accelerating object.

x

Another tangent. Another instantaneous velocity!

t

The tangent touches the curve at one point. Its slope gives the instantaneous velocity at that point.

x

v

a

t

t

t

Acceleration

vs

time

Position

vs

time

Velocity

vs

time

Summary:Constant position graphs

x

v

a

t

t

t

Acceleration

vs

time

Position

vs

time

Velocity

vs

time

Summary:Constant velocity graphs

x

v

a

t

t

t

Acceleration

vs

time

Position

vs

time

Velocity

vs

time

Summary:Constant acceleration graphs
Summary

v = vo + at

x = xo + vot + 1/2 at2

v2 = vo2 + 2a(∆x)

Free Fall
• Occurs when an object falls unimpeded.
• Gravity accelerates the object toward the earth.
Acceleration due to gravity
• g = 9.8 m/s2 downward.
• a = -g if up is positive.
• acceleration is down when ball is thrown up EVERYWHERE in the balls flight.
Summary

v = vo - gt

x = xo + vot - 1/2 gt2

v2 = vo2 – 2g(∆x)

Symmetry
• When something is thrown upward and returns to the thrower, this is very symmetric.
• The object spends half its time traveling up; half traveling down.
• Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with.
• Acceleration is –9.8 m/s2 everywhere!