PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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PHYSICS UNIT 1: KINEMATICS (Describing Motion). MOTION ALONG A LINE. Who’s Upside Down?. MOTION ALONG A LINE. Who’s Moving?. MOTION ALONG A LINE. Motion : change in position of an object compared to a frame of reference (a "stationary" reference point) Measuring Motion (along a line)

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MOTION ALONG A LINE
• Who’s Upside Down?
MOTION ALONG A LINE
• Who’s Moving?
MOTION ALONG A LINE
• Motion: change in position of an object compared toa frame of reference (a"stationary" reference point)
• Measuring Motion (along a line)
• position, x: location with respect to the origin The origin is (x=0), unit: m
• displacement, s = Dx : change in position

Dx = xf – xidisplacement = final position – initial position

MOTION ALONG A LINE
• displacement examples
MOTION ALONG A LINE
• time, t: time since motion start, unit: s (text uses Dt)
• velocity, v: time rate of displacement, unit: m/s
• average velocity, vav = (xf-xi)/t
• has same +/- sign as displacement – shows direction of motion along line
• instantaneous velocity, v: actual velocity at a specific point in time, slope on an x vs. t graph.
• at constant speed, v=vav
• for changing speed, vvav
MOTION ALONG A LINE
• Speed: the amount of velocity S=d/t
• Velocity is speed and direction (+/- along a line), speed doesn’t have direction. V=∆x/t
• a velocity of -24 m/s is not the same as +24 m/s (opposite directions), but both have the same speed (24 m/s).
• car speedometer indicates speed only; for velocity, you would need a speedometer and a compass.
SOLVING PROBLEMS
• Problem-Solving Strategy
• Given: What information does the problem give me?
• Question: What is the problem asking for?
• Equation: What equations or principles can I use to find what’s required?
• Solve: Figure out the answer.
• Check: Do the units work out correctly? Does the answer seem reasonable?
GRAPHING MOTION
• interpreting an x vs. t (position vs. time) graph

constant +v

constant v = 0

constant –v

changing +v

changing +v

(moving forward)

(slowing down)

(not moving)

(moving backward)

(speeding up)

x

t

GRAPHING MOTION
• interpreting an x vs. t (position vs. time) graph
• for linear x vs. t graphs:

slope =rise/run =Dx/Dt, so

rise = Dx

slope = vav

run = Dt

x

t

GRAPHING MOTION
• interpreting an x vs. t (position vs. time) graph
• for curving x vs. t graphs:

slope of tangent line = vinstantaneous

GRAPHING MOTION
• interpreting a v vs. t (velocity vs. time) graph

constant +v

constant v = 0

constant –v

changing +v

changing +v

(slowing down)

(moving backward)

(speeding up)

(not moving)

(moving forward)

GRAPHING MOTION
• comparing an x vs. t and a v vs. t graph
constant velocity

constant acceleration

ACCELERATION
ACCELERATION
• Acceleration, a: rate of change of velocity
• unit: (m/s)/s or m/s2
• speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?)
• average acceleration, aav = (v-u)/t= Dv/t
• instantaneous acceleration, a: actual acceleration at a specific point in time
time (s)

0

1

2

3

4

5

6

speed (m/s)

0

2

4

6

8

10

12

position (m)

0

1

4

9

16

25

36

ACCELERATION
• Constantacceleration (a = aav)

example: a=2 m/s2

v  t, x  t2

terms:

t: elapsed time

xf : final position

xo: initial position

s: change in position (xf-xi)

terms:

a: acceleration

vavg: average velocity

vf: final velocity

u, vo: initial velocity

Dv: change in velocity (v-u)

ACCELERATION
defined equations:

a = Dv/t

vav = Dx/t

vav = (v+u)/2

derived equations:

s = ½(v+u)t

v = u + at

xf = xi + ut + ½at2

v2 = u2 + 2as

ACCELERATION
GRAPHING MOTION
• interpreting a v vs. t (velocity vs. time) graph

For linear v vs. t graphs, slope = a

constant a = 0

constant –a

constant +a

(slowing down)

(speeding up)

(constant speed)

GRAPHING MOTION
• comparing v vs. t and a vs. t graphs

### PHYSICS

UNIT 1: KINEMATICS

(Describing Motion)

FREE FALL
• Free Fall: all falling objects are constantly accelerated due to gravity
• acceleration due to gravity, g, is the same for all objects
• use y instead of x, up is positive
• g = –9.80 m/s2(at sea level; decreases with altitude)
FREE FALL
• air resistance reduces acceleration to zero over long falls; reach constant, "terminal" velocity.
• Why does this occur?
• Air resistance is proportional to v^2

### PHYSICS

UNIT 1: KINEMATICS

(Describing Motion)

Start at the Old Lagoon

Go 50 paces East

Go 25 Paces North

Go 15 paces West

Go 30 paces North

Go 20 paces Southeast

X marks the Spot!

MOTION IN A PLANE
MOTION IN A PLANE
• Trigonometry
• sine: sin q = opp/hyp
• cosine: cos q = adj/hyp
• tangent: tan q = opp/adj
MOTION IN A PLANE
• Vectors
• scalars: only show how much (position, time, speed, mass)
• vectors: show how much and in what direction
• displacement, r or x : distance and direction
• velocity, v : speed and direction
• acceleration, a: change in speed and direction
q

v

N

E

W

S

MOTION IN A PLANE
• Vectors
• arrows:velocity vector v = v (speed), q(direction)
• length proportional to amount
• direction in map coordinates
• between poles, give degreesN of W, degrees S ofW, etc.
MOTION IN A PLANE

puck v relative to earth=puck v relative to table+table v relative to earth

MOTION IN A PLANE
• Combining Vectors
• draw a diagram & label the origin/axes!
• Collinear vectors: v1 v2 v1 v2
• resultant: vnet=v1+v2 (direction: + or –)
• ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity?
• ex: A plane flies 40 m/s E with a 10 m/s E tailwind. What is the net velocity?
MOTION IN A PLANE
• Perpendicular vectors:

resultant’s magnitude:

resultant’s direction:

### PHYSICS

UNIT 1: KINEMATICS

(Describing Motion)

UNIT 1 TEST PREVIEW
• Concepts Covered:
• motion, position, time
• speed (average, instantaneous)
• x vs. t graphs, v vs. t graphs, a vs. t graphs
• vectors, scalars, displacement, velocity
• adding collinear & perpendicular vectors
• acceleration
• free fall, air resistance
UNIT 1 TEST PREVIEW
• What’s On The Test:
• 21 multiple choice, 12 problems

Dx = ½(vf+vi)t vf = vi + at

xf = xi + vit + ½at2 vf2 = vi2 + 2aDx