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Warm UpDescribe what the V-T graph would look like for an object with negative acceleration when it starts with
a.) no velocityb.) positive velocityc.) negative velocity
Be sure to describe what will happen as time continues.
Bulletin BoardReadings
◦Pages 48-51Personal Practice
◦# 1-4 on page 55
The 5 Big Equations
0 1 2 3 4 5 605
1015202530
Time (s)
Posit
ion
(m
)
0 1 2 3 4 5 602468
1012
Time (s)
Velo
cit
y (
m/s
)
0 1 2 3 4 5 60
0.51
1.52
2.5
Time (s)
Accele
rati
on
(m
/s2
)
0 1 2 3 4 5 605
1015202530
Time (s)
Posit
ion
(m
)
0 1 2 3 4 5 602468
1012
Time (s)
Velo
cit
y (
m/s
)
0 1 2 3 4 5 60
0.51
1.52
2.5
Time (s)
Accele
rati
on
(m
/s2
)
A great graphical picture, but a lot of work to answer small questions.
The 5 Big Kinematic Equations
tavv if
davv if 222
22
1tatvd f
22
1tatvd i
tvv
d if
2
The 5 Big Kinematic Equations
tavv if
davv if 222
22
1tatvd f
22
1tatvd i
tvv
d if
2
These equations will help us pull the right information from our situation.
A CLOSER LOOK AT EACH ONE
How did we get these equations?How do we use these equations?
tavv if
tavv if
Definition of average Acceleration: t
va
tavv if
Definition of average Acceleration: t
vv
t
va if
tavv if
Definition of average Acceleration: t
vv
t
va if
Now Rearrange!
tavv if
From the graph
tavv if
0 1 2 3 4 5 60
2
4
6
8
10
12
Time (s)
Velo
cit
y (
m/s
)
iv
tavv if
0 1 2 3 4 5 60
2
4
6
8
10
12
Time (s)
Velo
cit
y (
m/s
)
iv
a
t
v
ExampleA car can accelerate at a rate of 5 m/s2. How long will it take for the car to reach 80 km/h?
ExampleA car can accelerate at a rate of 5 m/s2. How long will it take for the car to reach 80 km/h?
sa
vvtAnalyze
tavvLook
tAsked
smhkmvvaGiven
if
if
fi
44~4.440.5
02.22:
:
?:
/2.22/80,0,0.5:
Now you try (in groups)!A motorcycle with an initial velocity of 6.0 m/s [E] accelerates at 4.0 m/s2 [E]. How long will it take the motorcycle to reach a final velocity of 36.0 m/s [E]?
An elk moving at a velocity of 20 km/h [N] accelerates at 1.5 m/s2 [N] for 9.3 s until it reaches its maximum velocity. Calculate its maximum velocity, in km/h.
Start with:
&
tvv
d if
2
2if
avg
vvv
t
dvavg
Start with:
&
tvv
d if
2
2if
avg
vvv
t
dvavg
Put them together! t
dvv if
2
Start with:
&
tvv
d if
2
2if
avg
vvv
t
dvavg
Put them together! t
dvv if
2
And Rearrange!
tvv
d if
2
0 1 2 3 4 5 60
2
4
6
8
10
12
Time (s)
Velo
cit
y (
m/s
)
iv
fv
tvv
d if
2
0 1 2 3 4 5 60
2
4
6
8
10
12
Time (s)
Velo
cit
y (
m/s
)
avgv
Now you try (in groups)!A dog running at a velocity of 16 m/s [S] slows down uniformly to a velocity of 4.0 m/s [S] in 4.0 s. What is the displacement of the dog during this time?
A ball moves up a hill with an initial velocity of 3.0 m/s. Four seconds later, it is moving down the hill at 9.0 m/s. Find the displacement of the ball from its initial point of release.
Take what we know from the last equation:
22
1tatvd i
tvv
d if
2
Take what we know from the last equation:
22
1tatvd i
tvv
d if
2
Rearrange: tvvd if
2
Take what we know from the last equation:
22
1tatvd i
tvv
d if
2
Rearrange: tvvd if
2
Expand: tvtvd if
2
Expand: tvtvd if
2
Expand:
Use equation #1:
tvtvd if
2
tavv if
Expand:
Use equation #1:
tvtvd if
2
tavv if
To get: tvttavd ii
2
Expand:
Use equation #1:
tvtvd if
2
tavv if
To get: tvttavd ii
2
Now Expand & Rearrange!
22
1tatvd i
22
1tatvd i
0 1 2 3 4 5 60
2
4
6
8
10
12
Time (s)
Velo
cit
y (
m/s
)
Now you try (in groups)!A skier is moving down a uniform slope with an initial speed of 3.0 m/s. If the acceleration down the hill is 4.0 m/s2, find the skier’s displacement after 5.0 s.
A motorcycle is traveling at 100 km/h on a flat road. The rider applies the brakes to slow down the motorcycle at the rate of .80 m/s2 for 30 s. How far did the motorcycle travel during this time?
Group Experiment:
Question: What is the acceleration due to gravity?
Procedure:1.Hold a ball 3 meter high and time
how long it takes to reach the ground.
2.With this information and using the third equation, find the acceleration that the ball experienced.
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