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) Speed is the rate at which distance is
covered. Avg. speed = distance/time (m/s)
MOTION ALONG A LINE Distance, D: Distance is how far an
object moves, unit: m Time, t: time since motion start, unit:
s Velocity, v: is speed in a given
direction Ex. 30 m/s North
MOTION ALONG A LINE Instantaneous Speed: the speed at
any given instant. (This is what your speedometer reads)
SOLVING PROBLEMS Problem-Solving Strategy
Given: What information does the problem give me? S = 20 m/s t = 5 s
Question: What is the problem asking for?D = ?
Equation: What equations or principles can I use to find what’s required?
S=D/t Solve: Figure out the answer.
D=Sxt = 100m Check: Do the units work out correctly? Does the
answer seem reasonable?
Practice Two cars are traveling south on I-5. Car A
has an average speed of 20.0 m/s. Car B has an average speed of 30.0 m/s.
a. How much time does it take Car A to travel 1500 m?
b. How far does Car B travel in 30.0 s?75 s
900 m
LAB 1.1 QUIZ A student made the following
graph by moving in front of a motion sensor (the student was facing the sensor). Describe the student’s motion for each labeled section.a
b
c
d
e
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 = v
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)
ACCELERATION Acceleration, a: rate of change of
velocity unit: meter per second per second or m/s2
speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?)
average acceleration, aav = (vf-vi)/t = v/t
ACCELERATION Constant acceleration
example: a=2 m/s2 V = at D =1/2 a t2
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 terms:
t: elapsed timexf : final position
xi: initial position
x: change in position (xf-xi)
terms:a: accelerationvav: average
velocityvf: final velocity
vi: initial velocity
v: change in velocity (vf-vi)
ACCELERATION defined
equations:a = v/t vav = x/t
vav = (vf+vi)/2
derived equations:x = ½(vf+vi)t
vf = vi + at
xf = xi + vit + ½at2
vf2 = vi
2 + 2ax
QUIZ 1.3 A train traveling 25.0 m/s begins slowing
down with an acceleration of –4.00 m/s2. The train travels 50.0 m as it slows down (but it does NOT come to a stop).(a) What is its final velocity?(b) How much time does it take?(c) How far would the train have traveled in 5.00 s? Note: the train’s final velocity is NOT the same as it was in question (a)
15.0 m/s
2.50 s
75.0 m
GRAPHING MOTION
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
MOTION IN A PLANE Motion in a Plane vs.
Motion in a Line It’s like reading a
treasure map. Go 25 Paces North Go 15 paces West Go 30 paces North Go 20 paces Southeast X marks the Spot!
MOTION IN A PLANE Scalar Quantity: only shows how much
size or magnitude (distance, time, speed, mass)
Vector Quantity: shows how much size or magnitude and in what direction
displacement, r : 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
Examples of Vectors If a plane flies North at 100 m/s
and the wind blows North at 20 m/s. What is the resultant?
If a plane flies North at 100 m/s and the wind blows South at 20 m/s then what is the resultant
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?
Combining non linear vectors
What if the plane were to fly into a cross wind?
Ex. A plane flies North at 100 m/s and there is a 50 m/s Easterly wind. What is the plane’s net (combined) velocity?
MOTION IN A PLANE Perpendicular vectors:
vy
vx
v
2y
2x vvv
x
y1
v
vtan
resultant’s magnitude:
resultant’s direction:
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