Kinematics equations made simple

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Kinematics (equations made simple!)
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• For next time
• Read Chapter 2, Section 6
• Homework Chapter 2, Prob 24

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Review
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Are you going up or down?
Are you speeding up or slowing down?
a
v
What will your velocity be in 1 second?
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Review
0
Are you going up or down?
t0
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
a
4
Review
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Are you going up or down?
t1
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
5
Review
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Are you going up or down?
t2
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
6
Review
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Are you going up or down?
t3
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
7
Review
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Are you going up or down?
t4
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
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Review
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Are you going up or down?
t5
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
9
Review
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Are you going up or down?
t6
Are you speeding up or slowing down?
v
What will your velocity be in 1 second?
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Bungee Jumping
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Motion 1
0
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Motion 2
0
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Motion 3
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slowing
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Motion 4
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bottom
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Motion 5
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speeding up
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Motion 6
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Still rising
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Motion 7
0
top
18
0
1
5
2
6
3
7
4
bottom
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bungy-jumping is the most fun you'll never want
to have again.
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20
Who is passing who?
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• You see two cars side-by-side as they exit a
  tunnel on the freeway. The red car has
  velocity of 40 m/s and acceleration of 20
  m/s/s. The blue car has velocity of 20 m/s and
  acceleration of 40 m/s/s.Which car is passing
  the other the instant they leave the tunnel?

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Problem
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• A car has initial velocity 30 miles/hour. It
  accelerates at 2 miles/hour/s for 10 seconds.
  What is its final velocity?

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Equation 1
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• vf vo a ?t

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Problem
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• A child slides down a constant slope on a
  toboggan. When the child passes her older
  brother, he estimates her speed at 2 m/s. When
  she passes her younger brother 10 seconds later,
  he estimates her speed at 10 m/s. Estimate how
  far apart her brothers are standing.
• What is her average velocity?

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Equation 2
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• vf vo a ?t
• ?x 1/2 (vo vf) ?t

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And finally...
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• A return to the cart on the track. When last we
  met...

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0
Halfway in time or halfway in distance?
vo o
vf ?
Where does the instantaneous velocity equal that
average velocity?
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0
vf2vave
Velocity (m/s)
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3
2
4
5
1
6
0
Time (sec)
29
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Halfway in time or halfway in distance?
vo o
vf ?
Where does the instantaneous velocity equal that
average velocity?
30
0
Greater distance in first half or second half of
time?
vo o
vf ?
Where does the instantaneous velocity equal that
average velocity?
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Problem
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• A boat is cruising at 3 m/s. At time t0, the
  boat begins accelerating with a1.6 m/s/s. How
  far will the boat have traveled 10 seconds later?

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Which equation to use?
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• vf vo a?t
• ?x 1/2 (vo vf) ?t

Both !!
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Problem
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• A boat is cruising at 3 m/s. At time t0, the
  boat begins accelerating with a1.6 m/s/s. How
  far will the boat have traveled 10 seconds later?

• First what is the boats velocity after 10 s?
• What is the boats average velocity?
• How far did the boat travel?

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Now
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• vf vo a?t
• ?x 1/2 (vo vf) ?t
• ?x vo ?t 1/2 a ?t 2

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Finally
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• Variables
• ?x a vf vo ?t
• vf vo a ?t ? ? ? ?
• ?x 1/2 (vo vf) ?t ? ? ? ?
• ?x vo ?t 1/2 a ?t2 ? ? ?
  ?
• vf2 vo2 2a?x ? ? ? ?

On page 36 of your text.
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Problem
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• A boat is cruising at 3 m/s. At time t0, the
  boat begins accelerating with a1.6 m/s/s. How
  far will the boat have traveled 10 seconds later?

• What do we know?
• What dont we know?
• What dont we care about?

37
Recall
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• Variables
• ?x a vf vo ?t
• vf vo a ?t ? ? ? ?
• ?x 1/2 (vo vf) ?t ? ? ? ?
• ?x vo ?t 1/2 a ?t2 ? ? ?
  ?
• vf2 vo2 2a?x ? ? ? ?

On page 36 of your text.
38
Problem
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• A plane is cruising at 50 m/s. The plane
  suddenly begins accelerating with a4m/s/s until
  it reaches 90 m/s. How far does it travel in
  this time?

• What do we know?
• What dont we know?
• What dont we care about?

39
Recall
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• Variables
• ?x a vf vo ?t
• vf vo a ?t ? ? ? ?
• ?x 1/2 (vo vf) ?t ? ? ? ?
• ?x vo ?t 1/2 a ?t2 ? ? ?
  ?
• vf2 vo2 2a?x ? ? ? ?

On page 36 of your text.
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OR
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• A plane is cruising at 50 m/s. The plane
  suddenly begins accelerating with a4m/s/s until
  it reaches 90 m/s. How far does it travel in
  this time?

• How long does it take for the plane to reach 90
  m/s?
• What is the average velocity?
• What distance is covered?

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Problem
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• A skier, starting from rest, accelerates down a
  slope at 1.6 m/s/s. How far has she gone at the
  end of 5.0 seconds?

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Recall
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• Variables
• ?x a vf vo ?t
• vf vo a ?t ? ? ? ?
• ?x 1/2 (vo vf) ?t ? ? ? ?
• ?x vo ?t 1/2 a ?t2 ? ? ?
  ?
• vf2 vo2 2a?x ? ? ? ?

On page 36 of your text.