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) position, x: location with respect to the

origin The origin is (x=0), unit: m displacement, s = x : change in position

x = xf – xi displacement = final position – initial position

MOTION ALONG A LINE displacement examples

MOTION ALONG A LINE time, t: time since motion start, unit: s (text

uses t) 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, vvav

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?

x

(m)

t (s)

GRAPHING MOTION interpreting an x vs. t (position vs.

time) graph

(moving

forward)

constant +v

(not moving

)

constant v = 0

(moving backwar

d)

constant –v

changing +v

(speeding up)

changing +v

(slowing down)

GRAPHING MOTION interpreting an x vs. t (position vs. time)

graph for linear x vs. t graphs:

rise = x

x

trun = t

slope = rise/run = x/t, so slope = vav

GRAPHING MOTION interpreting an x vs. t (position vs. time)

graph for curving x vs. t graphs:x

t

slope of tangent line = vinstantaneous

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

graphv

(m/s)

t (s)

(moving

forward)

constant +v

(not moving

)

constant v = 0

(moving backward

)

constant –v

changing +v

(speeding up)

changing +v

(slowing down)

GRAPHING MOTION comparing an x vs. t and a v vs. t

graph

v

(m/s)

t (s)

ACCELERATION constant velocity constant

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 = v/t instantaneous acceleration, a: actual

acceleration at a specific point in time

ACCELERATION

Constant acceleration (a = aav)

example: a=2 m/s2 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

v t, x t2

ACCELERATION terms:

t: elapsed timexf : final position

xo: initial position

s: change in position (xf-xi)

terms:a: accelerationvavg: average

velocityvf: final velocity

u, vo: initial velocity

v: change in velocity (v-u)

ACCELERATION defined

equations:a = v/t vav = x/t

vav = (v+u)/2

derived equations: s = ½(v+u)t v = u + atxf = xi + ut +

½at2

v2 = u2 + 2as

v

(m/s)

t (s)

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

graph

(speeding up)

constant +a

(constant speed)

constant a = 0

(slowing down)

constant –a

For linear v vs. t graphs, slope = a

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

graphs

a(m/s ) t (s)

2

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)

MOTION IN A PLANE 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 Trigonometry

sine: sin = opp/hyp

cosine: cos = adj/hyp

tangent: tan = opp/adj

hypotenuse

oppositeside

adjacentside

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

MOTION IN A PLANE Vectors

arrows: velocity vector v = v (speed), (direction)

length proportional to amount direction in map coordinates

between poles, give degreesN of W, degrees S of W, etc.

N

S

W E

v

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:

vy

vx

v

2y

2x vvv

x

y1

v

vtan

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

x = ½(vf+vi)t vf = vi + at

xf = xi + vit + ½at2 vf2 = vi

2 + 2ax

%ErrorO A

A

100

2vv

v ifav

tx

txx

v ifav

tv

tvv

a ifav

2y

2x vvv

x

y1

v

vtan