Planning Ahead• Pay attention to “Free-Fall.”

• Homework, see the problems on the course

webpage. (Whether you get the right answer or

not, you still get the same points, provided that

you’ve demonstrated that you made a good

faith attempt at solving the problem. Also

attach any additional problems that you have

been working on).

Lecture Outline

• I. Motion Terminology

• II. Physics of the Sprinter

• III. Visualizing Motion

• Level III: Motion

Goals

• 1.) Interpret Motion Graphs.

• 2.) Understand the difference

between velocity and acceleration.

White Card – Check List

• 1. Identify the type of motion.

• 2. Sketch the motion (coordinate system).

• 3. Reasoning:

• 4. Find the Forces acting on the object.

• 5. Determine the acceleration of the object.

• 6. Write the Kinematics equations and solve.

• 7. Assess the answer.

Problem Solving Overview• Type of motion – determines the equation.

• Reasoning – determines the theory used to

explain the phenomenon.

• Sketch – determines the values that will go into

the equation.

• Coordinate system – determines if the values

are positive or negative. It also determines how

the graphs look.

Be consistent!

Review Physics Solution

Recall: Rules on Dimensions

𝑥 = 𝑦 + 𝑧

1. If x has dimensions of length, then y and z

must also have dimensions of length.

2. Most arguments in a function are unitless.

For example sin(x), log(x), e(x), all of the x

have no units.

Dimensions Drill/Due Today

𝐹 = 𝑚[? ]

If F has units of (kg × m/s2) and m has units

of kg, then what are the dimensions of [?]

A. m2

B. m/s2

C. m2/s2

D. None

Dimensions Drill/Due Today

𝐸 = 9800𝑘𝑔𝑚2

𝑠2𝑚 = 80𝑘𝑔

𝑔 = 10𝑚

𝑠2

Find the distance

Recall: Theory of Motion

– Newton’s First Law: (Inertia) Objects at rest

remain at rest unless acted upon by a net external

force; objects in motion remain in motion and

move in a straight line unless acted upon by a net

external force.

– Newton’s Second Law: F= ma

– Newton’s Third Law: For ever action there is an

Equal and Opposite action.

Known Key Equations

run

riseslope

heightbaseArea

Graphs Goals

)s(t

)s/m(vx

Slope = acceleration

displacement = area

Velocity vs. time graph

Key Concept Motion Graphs

)s(t )s(t )s(t

)m(x )s/m(vx )s/m(a 2

x

Displacement Velocity Acceleration

Slope = acceleration

displacement = area

Motion

acceleration

constantzero

stationary

Constant

velocity

Slowing

down

Momentarily

stopped

Speeding

up

Key Motion Equations

𝑥𝑓 = 𝑣𝑖𝑥𝑡 + 𝑥𝑖

𝑣𝑓𝑥 = 𝑣𝑖𝑥

If a = 0, thenIf a = constant

then

𝑥𝑓 =1

2𝑎𝑥𝑡

2 + 𝑣𝑖𝑥𝑡 + 𝑥𝑖

𝑣𝑓𝑥 = 𝑎𝑥𝑡 + 𝑣𝑖𝑥

From Newton’s 2nd Law F = ma:

The numbers put into the equation

come from the sketch.

x

t

t

v

Kinematics Equation

𝑥𝑓 = 𝑣𝑖𝑡 + 𝑥𝑖

𝑣𝑓 = 𝑣𝑖

If a = 0

then

If a = constant

then

𝑥𝑓 =1

2𝑎𝑥𝑡

2 + 𝑣𝑖𝑡 + 𝑥𝑖

𝑣𝑓 = 𝑎𝑥𝑡 + 𝑣𝑖

From Newton’s 2nd Law F = ma:

The numbers put into the equation

come from the sketch.

Displacement

xi xfO

0t t

𝑥𝑓 =1

2𝑎𝑥𝑡

2 + 𝑣𝑖𝑥𝑡 + 𝑥𝑖

𝑎𝑥 𝑎𝑥

𝑣𝑖𝑥 𝑣𝑓𝑥

Recall: Particle Model of Motion

MCAT Graphs

Which position-versus-time graph represents the motion shown in the motion diagram?

I. Motion Terminology• 1. Displacement

• 2. Velocity

• 3. Acceleration

Motion Terminology• Position: location of the object at a given time.

• Displacement:

• Distance: total distance traveled.

Origin fxix

if xxx

Position and Velocity• 1. The value of the slope from

the Position vs. time data is the

velocity (at that time).

• 2. The value of the area under the

slope of the velocity vs time

graph is the displacement of the

object in that time interval.

Velocity

• Velocity measures the displacement during

a time interval.

www.winstonmotorsports.com

Unit:

s

m

hr

mi

Dimensions

time

distance

or

Velocity

• Velocity is the rate of change of position.

velocity

Change in position

Change in time

Arrow indicates vector

റ𝑣 = ∆ റ𝑥

∆𝑡

റ𝑣

Which velocity-versus-time graph goes with the position-versus-time graph on the left?

Drill: Draw the Visualization of

this motion.

Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m.

Drill: Draw the Visualization of this motion.

Motion Drill/Due Today

Draw the velocity vs time graph.

po

siti

on

(m

)

Region I

Region II

Drill: Draw the Visualization of this motion.

Velocity and Acceleration

• 1. The value of the slope from

the Velocity vs. time data is the

acceleration.

• 2. The value of the area under

the slope of the acceleration vs

time graph is the velocity at that

time.

Acceleration

• Acceleration measures how much velocity

changes during a time interval.

www.winstonmotorsports.com

Acceleration

• Acceleration is the rate of change of velocity.

t

va

acceleration

Change in velocity

Change in time

a

Arrow indicates vector

Do You Know the Facts

• Which of the following is fatal to you?

• 10,000 mph

• 9.8 m/s2

• 100 mph

• 100 m/s2

• 100,000,000 m/s

Common Mistakes

• 9.8 m/s2 is a faster acceleration than 4

m/s2.

• Acceleration is not a speed nor velocity, so

words like fast or slow cannot be used.

• 9.8 m/s2 is a larger acceleration than 4

m/s2.

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Which velocity-versus-time graph or graphs goes with this acceleration-versus-time graph? The particle is initially moving to the right and eventually to the left.

Motion• Dynamics – branch of Mechanics that

deals with the motion of objects.

– Kinematics – study of motion without

regard to the forces producing it.

– Kinetics – the study of the forces that

produce or change motion. Motion is

caused by an unbalanced force acting on

a body.

Motion Graphs

)s(t )s(t )s(t

)m(x )s/m(vx )s/m(a 2

x

Displacement Velocity Acceleration

Slope = acceleration

displacement = area

Acceleration Drill/Due Today

• A car starts from the origin and

accelerates 6.0 m/s2 in the positive x-

direction. Draw the pictorial

representation of this problem.

Acceleration Sketch

xi=0 xf =? Origin

ft

2f,xs

m0.6a

2i,xs

m0.6a

0v i,x ?v f,x

Acceleration Drill/Due Today

• A car starts from the origin and

accelerates 6.0 m/s2 in the positive x-

direction. Explain this motion from

the Fundamental Laws of Motion.

Acceleration Drill/Due Today

• A car starts from the origin and

accelerates 6.0 m/s2 in the positive x-

direction. Draw the velocity vs time

and position vs time graphs for this

motion.

Acceleration Drill/Due Today

• A car starts from the origin and

accelerates 6.0 m/s2 in the positive x-

direction. Derive the velocity and

position equations for this motion.

Acceleration Drill/Due Today

• A car starts from the origin and

accelerates 6.0 m/s2 in the positive x-

direction.

• Predict the position of the car 3 s

later?

• What is the car’s velocity at 3 s?

Life Science Example• The speed of blood during one heart beat is

shown below. Approximate how far the blood

moves in one heart beat?

Life Science Example• Problem 18, page 62: The speed of blood during one heart beat is shown below. Approximate how far the blood moves in one

heart beat?

Reasoning: The

distance the blood

moves in one heart beat

is the area under the

curve between 0.2 and

0.4 s.

s

m75.0)s20.0(

2

1x m075.0

Assessment Drill/Due Today• Determine the magnitude of the acceleration

for both phases, speeding up and slowing

down.

Reasoning is?

Assessment Drill/Due Today• How many beats of heart will it take the blood

to get from your heart to brain?

Acceleration Drill/Due Today• A car starts from rest at the origin and

accelerates at 2 m/s2 for 8 s.

• Draw the pictorial representation for the

motion

• Explain the motion from the fundamental laws

of motion.

• Draw the x vs t and v vs t graphs.

• Write the two equations for this motion.

Motion Graphs

)s(t )s(t )s(t

)m(x )s/m(vx )s/m(a 2

x

Displacement Velocity Acceleration

Slope = acceleration

displacement = area

Life Science Drill/Due Today• When striking, the pike, a predatory fish,

can accelerate from rest to a speed of 4.0

m/s in 0.11 s.

• Draw a detailed sketch of this problem.

8:30

Motion Drill/Due Today• When striking, the pike, a predatory fish, can accelerate from rest to a speed of 4.0 m/s in 0.11 s.

• Draw a detailed sketch of this problem.

0x i xf = ?

t = 0.11s

𝑣𝑖 = 0 𝑣𝑓 = 4.0𝑚

𝑠𝑎𝑥 =?

Motion Drill/Due Today• When striking, the pike, a predatory fish,

can accelerate from rest to a speed of 4.0

m/s in 0.11 s.

• Draw a the velocity vs. time graph.

Motion Drill/Due Today• When striking, the pike, a predatory fish, can accelerate from rest to a speed of 4.0 m/s in 0.11 s.

• Draw a the velocity vs. time graph.

v

t0.11 s

4 𝑚

𝑠

Motion Drill/Due Today• When striking, the pike, a predatory fish,

can accelerate from rest to a speed of 4.0

m/s in 0.11 s.

• Determine the slope of the graph.

Motion Drill/Due Today• When striking, the pike, a predatory fish,

can accelerate from rest to a speed of 4.0

m/s in 0.11 s.

• Determine the area of the graph from 0 to

0.11s.

Motion Drill/Due Today• When striking, the pike, a predatory fish,

can accelerate from rest to a speed of 4.0

m/s in 0.11 s.

• Check the units.

Group Drill• A car accelerates from rest to a speed of 30.0 m/s in

5 s. Draw the velocity vs. time graph.

• What part of the graph contains information about the

acceleration?

• Determine the acceleration.

• What part of the graph contains information about

displacement?

• Determine the displacement.

• Use the acceleration you determined above in the

following equation: 2at2

1x