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PHYSICS 1L03
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Reza Nejat
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Physics

PHYSICS 1L03

Reza Nejat

Fall

Description

Motion
Kinematics
Locomotion
Chapter 2 What is motion?
Concepts: Position & Displacement
Velocity & Speed
Acceleration •Mtagfit.ie
Motion in one Dimension
Free Fall
Physiological Detection of Acceleration
PHYS 1L03, Fall 2013, McMaster University, R. Nejat
Motion Motion
http://www.imagekind.com/child-skipping-down-alley-art?IMID=642437f1-365b-4f63-988f-a5e712155344
A child skipping down alley. Can we analyze its motion?
Can we analyze its motion?
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
1 Motion Motion
The bird’s flight! The bird’s flight!
Q: What kind of A:
motion can you
verify for this bird’s
flight?
These images of a bird in flight show the bird’s What kind of motion can you verify for this bird’s flight?
position as a function of time.
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
Motion One-Dimensional (1D) Motion
•Im i,delti: •Piin
–Whereistheobject? –referstoanobjectlocationrelativetosome
•Position origin or reference point.
–Howfarhastheobjectmovedfromwhere
is was?
•Displacement
0 1 2 3 4 x1
–Howfastisthemotion?
1 2 4 x
•Velocity 0 3 2
–Isthemotiongettingfasterorslower?
sttih different in these two
•Acceleration coordinate systems with two different origins.
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
2 One-Dimensional Motion
One-Dimensional (1D) Motion
•Veordcarati:t
•Pive)r
–anobjectlocationrelative to some origin or
reference point, shown as a vector. •Veo:r is a quantity that has both a
magnitude and a direction.
▯
x –Positionisavectorquantity.
0 1 2 3 4 x1
▯
x •Sca:r is a quantity with no direction.
x2 –Themassofanobjectisascalarquantity.
-2 -1 0 1 2
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion One-Dimensional Motion
•Dilemete)r Distance:
octt•sc
–referstothechangein an object’s position along the actual path used to connect them.
▯ ▯ ▯
▯ x ▯ x ▯ x Displacement vs. Distance:
f i lfia ent of an object is not
the same as the distance it travels.
▯ x x
0 xi i x xf Example:
f x
▯ x ▯ x▯ x 0 xf xf xi
f i xi
▯ ▯ ▯
▯ x▯ xf▯xi
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
3 One-Dimensional (1D) Motion One-Dimensional Motion
•saemet
•OnDienilm)iabe
described by scalars (real numbers –Inonedimension(1D)
▯ x
with units) as functions of time.
–e.g. x(t)
x
0 xi xf
•Teiptrgi)es
track of direction. ▯ x ▯ x ▯fx i
• f stands for final and i stands for initial.
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion Motion
ailib coordinate system
•Dilm nt) ▯ x ▯ x ▯ f i
– indicates the motion is in the –ACoordinatesystem
▯ x ▯ 0 •hasii,l(unt)tiitinieco
positive x direction.
–Positionaxis
x x x •ilethatpassi,illtoghtheorg
0 i f the positive direction of motion
– ▯ x ▯ 0 indicates the motion is in the •In 1 D, this is called x-axis
negative x direction. •Thiiatx=0
–Timeaxis
0 xf xi x •hasii(t=l(s,ortinr),adrieco
indicating increasing value of time
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
4 Motion One-Dimensional Motion
X (cm)
•Cott:
•nuah:
T (s)
•Tgsw-e position of an object
as a function of time.
•jititte
increases.
•jeflts
decreases.
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion One-Dimensional Motion
Position vs time graph
Example: X(km) T(min)
•oit-e X(km) T(min)
+3 0 10
graph +3 0 +3 10
0
+3 10 +10 23
–Thepositionofatrainat +10 28
various time is given at the +10 23 -10
table, draw the position vs. 0 40
+10 28 -26 56 Position x (km)
time graph for it. -20
0 40
-26 56 -30
0 10 20 30 4050 60
Time t (min)
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
5 One-Dimensional Motion
One-Dimensional Motion
Average Velocity: defined as
Velocity: ▯ ▯ ▯
▯ x fx i ▯x
•it.r vaverage ▯
tf▯ t i ▯t
•ctofdittn
object is moving.
•tie rate of change of an object’s
displacement.
•Deedbtiemetd
the time interval
Position-versus-time graph
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion One-Dimensional Motion
▯ ▯ ▯
Average Velocity: vaveragexf▯xi▯ ▯x
f ▯ i ▯t Example:
x ▯ x ▯ x
vaverage 2 1 ▯ 41:3 tA .ot lHh uorht sespniart•A
t2▯ t1 ▯t p.m., the train is 3 km east of the city centre.
(omitting vector signs). B At 3:56 p.m., the train is 26 km west of the
•icil city centre. What is the average velocity of
slop of the straight line the train during this interval?
connecting two points
on the position vs time A
graph.
•fin v is m/s
PHYS 1L03, Fall 2013, McMaster University, R. Nejat graph PHYS 1L03, Fall 2013, McMaster University, R. Nejat
6 One-Dimensional Motion One-Dimensional Motion
Average speed:
Example:
distance distance
vavgspeed▯ ▯
t2▯ t 1 ▯t
•aid
– Is always positive
itira
speed (v avg)
•ti v is m/s
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion
One-Dimensional Motion
Instantaneous Velocity: Instantaneous Velocity: ▯ x d x
vins2 ) = slope of this line v ▯ lim ▯
(tangent to the carve) inst ▯t▯0 ▯ t d t
▯ x d x rrby
vinst ▯ ▯t▯0 ▯ the slope of a line x (m)
▯ t d t tangent to the
(omitting vector signs).
curve on the
position-versus-
nvil time graph
at any time is the slope
of a line tangent to the
position-versus-time
graph at that time.
t (sec)
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
7 One-Dimensional Motion One-Dimensional Motion
Example: Example:
• Use the position vs.
time graph for a train
to estimate its velocity
in km/h at t = 40 min.
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion One-Dimensional Motion
Example: Example:
elra•ieT a function of time is
given by the curve shown below. Find the velocity at t=2 s?
instantaneous velocity at time t = 2 s. When is the
velocity greatest? When is it zero? Is it ever
negative? What is the average velocity of this
particle between t = 2 s and t = 5s?
Greatest velocity ?
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
8 One-Dimensional Motion
One-Dimensional Motion
Example:
Zero velocity?
Negative velocity?
Average velocity?
tig peed, how an African lion
can catch a Cape buffalo?
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion
One-Dimensional Motion
Acceleration: •AAtlc
▯ ▯ ▯
▯ vf i ▯v vf
•etr . aaverage▯ Xf
f i t ▯
•chwsihitc
an object’s velocity is changing. •Ictl
▯
•i rate of change of velocity. ▯ ▯ v Xi vi
ainst▯ ▯t▯0 t t
▯t i fi
•Dpnobtydte
time interval.
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
9 One-Dimensional Motion One-Dimensional Motion
•Agtlc
•Aaeilt: v 2▯ v1 ▯ v
v2▯ v 1 ▯v a avg▯ ▯
a average ▯ t2▯ 1 ▯t
t2▯ t1 ▯t v2 •Ieyd
the slope of the
(omitting vector signs) velocity
straight line
•Iitl connecting two
B
▯v points on the v2 velocvty
ainst▯ ▯t▯0 v1 velocity-versus-time v1 A
▯t time
graph. 1 t2
(omitting vector signs)
2
• Unit of a is m/s
PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat
One-Dimensional Motion One-Dimensional Motion
B C D
▯ v Example: x
•toclt: ainst lim
▯t▯0▯t •rs x(t), v(t), a(t)
• The position-versus-time E
peby A t
the slope of a line graph of an object
moving along x-axis is v
tangent to the given.
curve on the t
aA
velocity-versus- A B aB – Draw the velocity-
time graph. versus time graph, v(t).
a
– Draw the acceleration- t
versus-time graph, a(t).
PHYS 1L03, Fall 2013, McMaster

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