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 = Dx : change in position
Dx = 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 Dt)
velocity, v: time rate of displacement, unit: m/s
 average velocity, v
av = (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=v
av
 for changing speed, vv
av
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
x
(m)
t (s)
constant constant constant
+v
v=0
–v
(moving
forward)
changing
+v
changing
+v
(not
(moving (speeding (slowing
down)
moving) backward)
up)
GRAPHING MOTION

interpreting an x vs. t (position vs. time) graph
 for linear x vs. t graphs:
x
slope =
rise/run
= Dx/Dt,
so
rise = Dx
slope = vav
run = Dt
t
GRAPHING MOTION

interpreting an x vs. t (position vs. time) graph
 for curving x vs. t graphs:
x
slope of
tangent line =
vinstantaneous
t
GRAPHING MOTION

interpreting a v vs. t (velocity vs. time) graph
v
(m/ s)
t (s)
constant constant constant
+v
v=0
–v
(moving
forward)
(not
moving)
(moving
backward)
changing
+v
changing
+v
(speeding (slowing
down)
up)
GRAPHING MOTION

comparing an x vs. t and a v vs. t graph
x
(m)
t (s)
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 = Dv/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
)
0
2
4
6
8
10
12
position (m)
0
1
4
9
16
25
36
speed (m/s
v  t, x  t2
ACCELERATION

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
GRAPHING MOTION

interpreting a v vs. t (velocity vs. time) graph
v
(m/ s)
t (s)
constant +a constant a
=0
(speeding
(constant
up)
speed)
constant –a
(slowing
down)
For
linear v
vs. t
graphs,
slope =
a
GRAPHING MOTION

comparing v vs. t and a vs. t graphs
v
(m/ s)
t (s)
a
2
(m/s )
t (s)
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
2
 g = –9.80 m/s (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
MOTION IN A PLANE

Trigonometry
sine:
sin q =
opp/hyp
 cosine:
cos q =
adj/hyp
 tangent:
tan q =
opp/adj

hypotenuse
q
adjacent
side
opposite
side
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

q
v
arrows: velocity vector
v = v (speed), q (direction)
N
 length proportional to amount
 direction in map coordinates
E
W
 between poles, give degrees
S
N of W, degrees S of W, etc.
MOTION IN A PLANE
puck v
relative to
earth
=
puck v
relative to
table
+
table v
MOTION IN A PLANE

Combining Vectors


draw a diagram & label the origin/axes!
Collinear vectors:
v1
v2
v1
v2
 resultant: v
(direction: + or –)
net=v1+v2
 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:
vx
v
q
vy
2
vx

2
vy
resultant’s direction:
v
v
 1 y 
q  tan  
 vx 
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:

%Error 
21 multiple choice, 12 problems
vf  vi
vav 
2
vf  vi D v
aav 

t
t
v

2
vy
v
 1 y 
q  tan  
 vx 
A
 100
xf  xi D x
vav 

t
t
Dx = ½(vf+vi)t
vf = vi + at
xf = xi + vit + ½at2 vf2 = vi2 + 2aDx
2
vx
O A