Kinematics (Stuff moving) (stuff). Daddy Definitions

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.