PHYSICS UNIT 1: KINEMATICS (Describing Motion)
Apr 01, 2015
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