Kinematics

(Stuff moving)

(stuff)

Start with vocabulary

• Position (x)– where it is (meters)• Displacement (x)– how far it moved,

direction (+/-) is important (meters)• Velocity – (v) how fast it moves, direction

is important (+/-) (meters/second)– Instantaneous, right now! Slope of tangent

• Average velocity – change in position divided by change in time

Vocabulary, continued

• Acceleration (a) – rate of change in velocity– m/s2

– Instantaneous, Slope of velocity time curve– Average, over time interval– Our equations apply only to constant

acceleration– When acceleration changes, we break the

problem into chunks of constant acceleration

The Equations!

20 0

1

2x x v t at

xv

t

va

t

0( )

2fv v

x t

2 20 2fv v a x

0v v at

All you get on AP Equations SheetDon’t forget these definitions!

Daddy

dva

dt

20 0

1

2x x v t at

0v v at

Mommy

2 20 2fv v a x

Notice no time in this one!

The area of a velocity “curve” is displacement!

0( )

2fv v

x t

v

t

Avg velocityarea

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… x=10m, t=10 s

• …reaches a maximum height– velocity at hmax = zero!

The Equations!

20 0

1

2x x v t at

dv

t

t

va

0( )

2fv v

x t

2 20 2fv v a x

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: vavg=??

xv

t

402.34

33.63211.963

mv

s

Given: x= 402 .34 meters in t=11.963 sec.

Principle: Kinematics(where to look for eq’n)

Equation:

Picture:

Simplify/Solve/Substitute

Drag Race #2

Unknown: aavg=??

2 20 2fv v a x

Given: vf= 40.73 m/s in x=201.17m

Principle: Kinematics(where to look for eq’n)

Equation:

Picture:

Simplify/Solve/Substitute

22

2

40.734.123

2 2 201.17fv m

ax s

zero

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 earth. Do yourself a favor and call down negative.

• 2) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach?

• 3) 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

More examples

• More example problems

• Try: v0=-3.0, a=5, t=4, x=?

• Try a “spike” (as in football player’s touchdown celebration)– xf=-5.0, x0=2.0, v0=-1.0, a=-9.8, t=?

The Equations!

20 0

1

2x x v t at

dv

t

t

va

0( )

2fv v

x t

2 20 2fv v a x

0v v at

Don’t forget definitions