### The Four Kinematic Equations

```Oct. 30, 2012
AGENDA:
1 – Bell Ringer
2 – Kinematics Equations
3 – Exit Ticket
Today’s Goal:
Students will be able to
identify which kinematic
equation to apply in each
situation
Homework
1. Pages 4-6
CHAMPS for Bell Ringer
C – Conversation – No Talking
H – Help – RAISE HAND for questions
A – Activity – Solve Bell Ringer on binder paper.
Homework out on desk
M – Materials and Movement – Pen/Pencil,
Notebook or Paper
P – Participation – Be in assigned seats, work
silently
S – Success – Get a stamp! I will collect!
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
4 MINUTES
REMAINING…
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
3 MINUTES
REMAINING…
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
2 MINUTES
REMAINING…
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
1minute Remaining…
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
30 Seconds Remaining…
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
BELLRINGER
TIME IS
UP!
October 30th (p. 13)
Objective:
Bell Ringer:
Students will be
How many quantities did we
able to identify
underline in each problem?
which kinematic
How many known variables are you
equation to
given in each problem?
apply in each
How many unknown variables are
situation
you asked to find in each problem?
How do you decide what equation to
use?
What do the equations mean to you?
1.
2.
3.
4.
5.
Shout Outs
Period 5 – Chris
Period 7 – Latifah, Shawn
Oct. 30, 2012
AGENDA:
1 – Bell Ringer
2 – Kinematics Equations
3 – Exit Ticket
Today’s Goal:
Students will be able to
identify which kinematic
equation to apply in each
situation
Homework
1. Pages 4-6
Week 8
Weekly Agenda
Monday – Kinematic Equations I
Tuesday – Kinematic Equations II
Wednesday – Kinematic Equations III
Thursday – Review
Friday – Review
Unit Test next week!
What are equations?
Equations are relationships.
Equations describe our world.
Equations have changed the course of history.
CHAMPS for Problems p. 4-6
C – Conversation – No Talking unless directed to
work in groups
H – Help – RAISE HAND for questions
A – Activity – Solve Problems on Page 4-6
M – Materials and Movement – Pen/Pencil, Packet
Pages 4-6
P – Participation – Complete Page 4-6
S – Success – Understand all Problems
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Solving Problems: THE EASY WAY (p. 4)
Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. What is the final velocity
vi = 0 m/s
a = 3 m/s2
Δt = 10 seconds
vf = ?
1.
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Solving Problems: THE EASY WAY (p. 4)
Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. What is the final velocity
vi = 0 m/s a = 3 m/s2 Δt = 10 seconds vf = ?
vf = vi + aΔt
1.
Solving Problems: THE EASY WAY (p. 4)
Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. What is the final velocity
vi = 0 m/s a = 3 m/s2 Δt = 10 seconds vf = ?
vf = vi + aΔt
vf = 0 m/s + (3 m/s2)(10 s) =
1.
Solving Problems: THE EASY WAY (p. 4)
Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. What is the final velocity
vi = 0 m/s a = 3 m/s2 Δt = 10 seconds vf = ?
vf = vi + aΔt
vf = 0 m/s + (3)(10) = 30 m/s
1.
Solving Problems: THE EASY WAY (p. 4
2. Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. How far does the Road
Runner travel during the ten second time interval?
vi = 0 m/s a = 3 m/s2 Δt = 10 seconds Δx = ?
Δx = viΔt + aΔt2
2
Solving Problems: THE EASY WAY (p. 4)
2. Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. How far does the Road
Runner travel during the ten second time interval?
vi = 0 m/s a = 3 m/s2 Δt = 10 seconds Δx = ?
Δx = viΔt + aΔt2
2
Δx = (0)(10) + (3)(10)2
2
Solving Problems: THE EASY WAY (p. 4)
2. Starting from rest, the Road Runner accelerates at
3 m/s2 for ten seconds. How far does the Road
Runner travel during the ten second time interval?
vi = 0 m/s a = 3 m/s2 Δt = 10 seconds Δx = ?
Δx = viΔt + aΔt2
2
Δx = (0)(10) + (3)(10)2
2
Δx = 0 + 150 m = 150 m
Solving Problems: THE EASY WAY (p. 4
3. A bullet starting from rest accelerates at 40,000
m/s2 down a 0.5 m long barrel. What is the velocity
of the bullet as it leaves the barrel of the gun?
vi = 0 m/s a = 40,000 m/s2 Δx = 0.5 m vf = ?
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Solving Problems (p. 4)
3. A bullet starting from rest accelerates at 40,000
m/s2 down a 0.5 m long barrel. What is the velocity
of the bullet as it leaves the barrel of the gun?
vi = 0 m/s a = 40,000 m/s2 Δx = 0.5 m vf = ?
vf2 = vi2 + 2aΔx
Solving Problems (p. 4)
3. A bullet starting from rest accelerates at 40,000
m/s2 down a 0.5 m long barrel. What is the velocity
of the bullet as it leaves the barrel of the gun?
vi = 0 m/s a = 40,000 m/s2 Δx = 0.5 m vf = ?
vf2 = vi2 + 2aΔx
vf2 = (0)2 + 2(40,000)(0.5)
Solving Problems (p. 4)
3. A bullet starting from rest accelerates at 40,000
m/s2 down a 0.5 m long barrel. What is the velocity
of the bullet as it leaves the barrel of the gun?
vi = 0 m/s a = 40,000 m/s2 Δx = 0.5 m vf = ?
vf2 = vi2 + 2aΔx
vf2 = (0)2 + 2(40,000)(0.5)
vf2 = 40,000
vf = 200 m/s
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
vf = vi + aΔt
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
vf = vi + aΔt
0 = 20 + 4a
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
vf = vi + aΔt
0 = 20 + 4a
0 = 20 + 4a
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
vf = vi + aΔt
0 = 20 + 4a
-20 + 0 = 20 + 4a + -20
-20 = 4a
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
vf = vi + aΔt
0 = 20 + 4a
-20 + 0 = 20 + 4a + -20
-20/4 = 4a/4
Solving Problems (p. 4)
4. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. What is the
acceleration of the car?
vi = 20 m/s vf = 0 m/s Δt = 4 seconds a = ?
vf = vi + aΔt
0 = 20 + 4a
-20 + 0 = 20 + 4a + -20
-20/4 = 4a/4
a = -5 m/s2
Solving Problems (p. 5)
5. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. How far does the car
travel before coming to a stop?
vi = 20 m/s vf = 0 m/s Δt = 4s Δx = ?
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Solving Problems (p. 5)
5. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. How far does the car
travel before coming to a stop?
vi = 20 m/s vf = 0 m/s Δt = 4s Δx = ?
Δx = (vf + vi)Δt
2
Solving Problems (p. 5)
5. A car traveling at 20 m/s applies its brakes and
comes to a stop in four seconds. How far does the car
travel before coming to a stop?
vi = 20 m/s vf = 0 m/s Δt = 4s Δx = ?
Δx = (vf + vi)Δt = (0 + 20)(4) = 40 m
2
2
Solving Problems (p. 5)
6. The USS Enterprise accelerates from rest at
100,000 m/s2 for a time of four seconds. How far
did the ship travel in that time?
Solving Problems (p. 5)
6. The USS Enterprise accelerates from rest at
100,000 m/s2 for a time of four seconds. How far
did the ship travel in that time?
vi = 0 m/s a = 100,000 m/s2 Δt = 4s Δx = ?
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Notes: Kinematic Equations
The Four Kinematic Equations:
vf = vi + aΔt
Δx = viΔt + aΔt2
2
vf2 = vi2 + 2aΔx
Δx = (vf + vi)Δt
2
Solving Problems (p. 5)
6. The USS Enterprise accelerates from rest at
100,000 m/s2 for a time of four seconds. How far
did the ship travel in that time?
vi = 0 m/s a = 100,000 m/s2 Δt = 4s Δx = ?
Δx = viΔt + aΔt2 =
2
Solving Problems (p. 5)
6. The USS Enterprise accelerates from rest at
100,000 m/s2 for a time of four seconds. How far
did the ship travel in that time?
vi = 0 m/s a = 100,000 m/s2 Δt = 4s Δx = ?
Δx = viΔt + aΔt2 = (0)(4) + (100,000)(4)2
2
2
Solving Problems (p. 5)
6. The USS Enterprise accelerates from rest at
100,000 m/s2 for a time of four seconds. How far
did the ship travel in that time?
vi = 0 m/s a = 100,000 m/s2 Δt = 4s Δx = ?
Δx = viΔt + aΔt2 = (0)(4) + (100,000)(4)2
2
2
Δx = 800,000 m
Solving Problems (p. 5)
7. At the scene of an accident, a police officer notices
that the skid marks of a car are 10 m long. The officer
knows that the typical deceleration of this car when
skidding is -45 m/s2. What can the officer estimate
the original speed of the car?
Solving Problems (p. 5)
7. At the scene of an accident, a police officer notices
that the skid marks of a car are 10 m long. The officer
knows that the typical deceleration of this car when
skidding is -45 m/s2. What can the officer estimate
the original speed of the car?
Solving Problems (p. 5)
7. At the scene of an accident, a police officer notices
that the skid marks of a car are 10 m long. The officer
knows that the typical deceleration of this car when
skidding is -45 m/s2. What can the officer estimate
the original speed of the car?
Δx = 10 m a = -45 m/s2 vf = 0 m/s vi = ?
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