C. Acceleration• Acceleration

– the rate of change of velocity– change in speed or direction

t

vva if

a: acceleration

vf: final velocity

vi: initial velocity

t: time

a

vf - vi

t

C. Acceleration

• Positive acceleration–“speeding up”

Negative acceleration “slowing down”

D. CalculationsYour neighbor skates at a speed of 4 m/s.

You can skate 100 m in 20 s. Who skates faster?

GIVEN:

d = 100 m

t = 20 s

v = ?

WORK:

v = d ÷ t

v = (100 m) ÷ (20 s)

v = 5 m/s

You skate faster!vd

t

D. CalculationsA roller coaster starts down a hill at 10 m/s.

Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?

GIVEN:

vi = 10 m/s

t = 3 s

vf = 32 m/s

a = ?

WORK:

a = (vf - vi) ÷ t

a = (32m/s - 10m/s) ÷ (3s)

a = 22 m/s ÷ 3 s

a = 7.3 m/s2a

vf - vi

t

D. CalculationsSound travels 330 m/s. If a lightning bolt

strikes the ground 1 km away from you, how long will it take for you to hear it?

GIVEN:

v = 330 m/s

d = 1km = 1000m

t = ?

WORK:

t = d ÷ v

t = (1000 m) ÷ (330 m/s)

t = 3.03 s

vd

t

D. CalculationsD. CalculationsHow long will it take a car traveling 30 m/s

to come to a stop if its acceleration is -3 m/s2?

GIVEN:

t = ?

vi = 30 m/s

vf = 0 m/s

a = -3 m/s2

WORK:

t = (vf - vi) ÷ a

t = (0m/s-30m/s)÷(-3m/s2)

t = -30 m/s ÷ -3m/s2

t = 10 sa

vf - vi

t

E. Graphing Motion

• slope =

• steeper slope =

• straight line =

• flat line =

Distance-Time Graph

A

B

faster speed

constant speed

no motion

speed

E. Graphing Motion

• Who started out faster?– A (steeper slope)

• Who had a constant speed?– A

• Describe B from 10-20 min.– B stopped moving

• Find their average speeds.– A = (2400m) ÷ (30min)

A = 80 m/min– B = (1200m) ÷ (30min) B

= 40 m/min

Distance-Time Graph

A

B

0

100

200

300

400

0 5 10 15 20

Time (s)

Dis

tan

ce (

m)

Distance-Time Graph

E. Graphing Motion

• Acceleration is indicated by a curve on a Distance-Time graph.

• Changing slope = changing velocity

E. Graphing Motion

• slope =

• straight line =

• flat line =0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

Speed-Time Graph

acceleration +ve = speeds up -ve = slows down

constant accel.

no accel. (constant velocity)

E. Graphing Motion

Specify the time period when the object was...

• slowing down– 5 to 10 seconds

• speeding up– 0 to 3 seconds

• moving at a constant speed– 3 to 5 seconds

• not moving– 0 & 10 seconds

0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

Speed-Time Graph

III. Defining Force Force

Newton’s First Law Friction

A. Force• Force

– a push or pull that one body exerts on another

– What forces are being exerted on the football?

Fkick

Fgrav

A. Force• Balanced Forces

– forces acting on an object that are opposite in direction and equal in size

–no change in velocity

A. Force• Net Force

–unbalanced forces that are not opposite and equal

–velocity changes (object accelerates)

Ffriction

W

Fpull

Fnet

NN

B. Newton’s First Law

• Newton’s First Law of Motion– An object at rest will remain at rest and an

object in motion will continue moving at a constant velocity unless acted upon by a net force.

B. Newton’s First Law• Newton’s First Law of Motion

– “Law of Inertia”

• Inertia– tendency of an object to resist any change

in its motion– increases as mass increases

ConcepTest 1TRUE or FALSE?

The object shown in the diagram must be at rest since there is no net force acting on it.

FALSE! A net force does not cause motion. A net force causes a change in motion, or acceleration.

ConcepTest 2You are a passenger in a car and not wearing your seat belt.

Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door.

Which is the correct analysis of the situation? ...

ConcepTest 21. Before and after the collision, there is a

rightward force pushing you into the door.

2. Starting at the time of collision, the door exerts a leftward force on you.

3. both of the above

4. neither of the above2. Starting at the time of collision, the

door exerts a leftward force on you.

C. Friction

• Friction– force that opposes motion between 2

surfaces–depends on the:

• types of surfaces• force between the surfaces

C. Friction• Friction is greater...

–between rough surfaces–when there’s a greater

force between the surfaces (e.g. more weight)

• Pros and Cons?

Ch. 3 & 4Motion & Forces

IV. Force & Acceleration Newton’s Second Law

Gravity Air Resistance Calculations

A. Newton’s Second Law

• Newton’s Second Law of Motion–The acceleration of an object is directly

proportional to the net force acting on it and inversely proportional to its mass.

F = ma

A. Newton’s Second Law

F = maF: force (N)m: mass (kg)a: accel (m/s2)

1 N = 1 kg ·m/s2

am

F

a

Fm

B. Gravity• Gravity

– force of attraction between any two objects in the universe

– increases as...• mass increases• distance decreases

B. Gravity• Who experiences more gravity - the

astronaut or the politician?

less distance

more mass

Which exerts more gravity - the Earth or the moon?

B. Gravity• Weight

– the force of gravity on an object

MASSalways the same

(kg)

WEIGHTdepends on gravity

(N)

W = mgW: weight (N)m: mass (kg)g: acceleration due

to gravity (m/s2)

W: weight (N)m: mass (kg)g: acceleration due

to gravity (m/s2)

W: weight (N)m: mass (kg)g: acceleration due

to gravity (m/s2)

B. Gravity• Would you weigh more on Earth or

Jupiter?

greater gravity

greater weight

greater mass

Jupiter because...

B. Gravity• Accel. due to gravity (g)

In the absence of air resistance, all falling objects have the same acceleration!

On Earth: g = 9.8 m/s2

mW

g

elephant

m

Wg

feather

C. Air Resistance• Air Resistance

–a.k.a. “fluid friction” or “drag”– force that air exerts on a moving

object to oppose its motion –depends on:

• speed• surface area• shape• density of fluid

C. Air Resistance• Terminal Velocity

–maximum velocity reached by a falling object

– reached when… Fgrav = Fair

Fair

Fgrav

no net force no acceleration constant velocity

C. Air Resistance• Terminal Velocity

increasing speed increasing air resistance until…

Fair = FgravAnimation from “Multimedia Physics Studios.”

C. Air Resistance

• Falling with air resistance

Fgrav = Fair

Animation from “Multimedia Physics Studios.”

heavier objects fall faster because they accelerate to higher speeds before reaching terminal velocity

larger Fgrav

need larger Fair

need higher speed

D. CalculationsWhat force would be required to

accelerate a 40 kg mass by 4 m/s2?

GIVEN:

F = ?

m = 40 kg

a = 4 m/s2

WORK:

F = ma

F = (40 kg)(4 m/s2)

F = 160 N

m

F

a

D. CalculationsA 4.0 kg shotput is thrown with 30 N of

force. What is its acceleration?

GIVEN:

m = 4.0 kg

F = 30 N

a = ?

WORK:

a = F ÷ m

a = (30 N) ÷ (4.0 kg)

a = 7.5 m/s2

m

F

a

D. CalculationsMrs. J. weighs 557 N. What is her

mass?

GIVEN:

F(W) = 557 N

m = ?

a(g) = 9.8 m/s2

WORK:

m = F ÷ a

m = (557 N) ÷ (9.8 m/s2)

m = 56.8 kg

m

F

a

ConcepTest• Is the following statement true or false?

– An astronaut has less mass on the moon since the moon exerts a weaker gravitational force.

False! Mass does not depend on gravity, weight does. The astronaut has less weight on the moon.