kinematics (stuff moving) (stuff). daddy definitions
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Kinematics
(Stuff moving)
(stuff)
Daddy
dva
dt
20 0
1
2d d v t at
0v v at
Definitions
dva
dt
dv
t
va
t
( )d
v positiondt
Mommy
2 20 2fv v a d
Notice no time in this one!
One more!
0( )
2fv v
d t
v
t
0( )
2fv v
x t
Avg velocity
Tips for deciphering word problems
• …at rest, …from rest – not moving at beginning… v0 = zero!
• ..comes to rest… vf=zero
• …Travels 10 m in 10 sec…– xf=10m, t=10 s
• …reaches a maximum height– velocity at hmax = zero!
The Equations!
20 0
1
2d d v t at
dv
t
va
t
0( )
2fv v
d t
2 20 2fv v a d
0v v at
Kinematics Examples
• Drag race– Avg velocity given time and disp– Avg acceleration given final v and disp
• Motion Graphing– Aircraft Catapult
• Draw position and acceleration given velocity
Drag Race
1. A car travels 402 .34 meters in 11.963 sec. What is its average velocity?
2. The same car reached 40.73 m/s at the end of the first 201.17 meters. What was its average acceleration?
Drag Race #1
Unknown:
Given:
Principle:
Equation:
Picture:
Simplify/Solve/Substitute
Drag Race #2
Unknown:
Given:
Principle:
Equation:
Picture:
Simplify/Solve/Substitute
Aircraft catapult
• Navy aircraft are launched from the decks of aircraft carriers with a steam powered catapult. The graph shows the velocity of the aircraft as a function of time. Analyze the graph and draw corresponding position and acceleration graphs.
Aircraft Catapult(v)
50
v(m/s)
time(s)5
Aircraft Catapult(a)
20
a(m/s2)
time(s)5
Aircraft Catapult(x)x(m)
time(s)
100
5
300
200
Freefall
• Same kinematics equations…
• Just constant acceleration of
a=g=9.8 m/s2
• toward mother earth.
• 1) A ball is dropped from 10 meters high. How fast is it going when it hits the ground?
• 2) How long does it take to reach the ground?
Freefall Example
• 3) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach?
• 4) How long does it take to reach this max height?
Freefall Example
• 5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from?
Freefall Example
Freefall Cases
• Downy– Dropping or “spiking”
• Uppy– Toss up
• Uppy – downy– Toss up off a ledge, object lands lower than the
ledge
Establish your coordinate system and be consistent with signs.
Wrap up
• Givens
• Unknowns
• P&P
• E– Time or none given
• S & S & S
The Equations!
20 0
1
2d d v t at
dv
t
va
t
0( )
2fv v
d t
2 20 2fv v a d
0v v at
• 5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from?
Freefall Example
Freefall Cases
• Downy– Dropping or “spiking”
• Uppy– Toss up
• Uppy – downy– Toss up off a ledge, object lands lower than the
ledge
Establish your coordinate system and be consistent with signs.
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