Chapter 2
LINEAR KINEMATICS
DESCRIBING OBJECTS IN MOTION
Define Motion:
Motion
is a change in
position over a period of
time.
Space and Time
Types of Motion
 Linear Motion (translation)
 all points on the body move
the same distance
 in the same direction
 at the same time


Rectilinear and Curvilinear
Linear Motion

Rectilinear Translation: straight line

figure skater gliding across the ice
Linear Motion

Curvilinear Motion: curved line

free-fall in sky-diving

Simultaneous motion in x & y directions
• Horizontal and vertical motion superimposed
Types of Motion
 Angular Motion (rotation)
 All points on the body move


Whole body rotation


through the same angle
giant swing, pirouette
Segment rotation

flexion, abduction, …
Types of Motion
 General Motion
 combines angular & linear motion
 most common
pedaling a bike
 walking
 drawing a straight line

Large Motions
Large Motions
Small Movement
Linear Kinematics
 Study of the time and space factors of motion
Linear Kinematic Quantities
 Kinematics is the form, pattern, or sequencing of movement
with respect to time.
 Kinematics spans both qualitative and quantitative form of
analysis.
Linear Kinematic Quantities
 For example, qualitatively describing the kinematics of a
soccer kick entails identifying

the major joint actions,
including hip flexion,
 knee extension,
 and possibly plantar flexion at the ankle.

Linear Kinematic Quantities
 A more detailed qualitative kinematic analysis might also
describe the precise sequencing and timing of body segment
movements, which translates to the degree of skill evident
on the part of the kicker.
Linear Kinematic Quantities
 Although most assessments of human movement are
carried out qualitatively through visual observation,
quantitative analysis is also sometimes appropriate.
Linear Kinematic Quantities
 Physical therapists, for example, often measure the range of
motion of an injured joint to help determine the extent to
which range of motion exercises may be needed.
Linear Kinematic Quantities
 When a coach measures an athlete's performance in the
shot put or long jump, this too is a quantitative assessment.
Linear Kinematics
Description of Linear Motion
How
far?
What direction?
How fast?
Speeding up, slowing down?
Position
 Identifying location in space
 At the start of movement?
 At the end of movement?
 At a specific time in the midst of movement?
 Use a fixed reference point
 1 dimension


starting line, finish line
2 dimension
Bloomington-Normal: north, east, south, west
 (goal line, sideline), (0,0), Cartesian coordinate system

Cartesian Coordinate System
Z
direction
X direction
(0,0,0)
Y direction
Research & Gait Analysis
Linear Kinematic Quantities
 Constructing a model performance.
 Scalar and vector quantities.
Linear Kinematic Quantities
 Displacement - change in position.
 Distance - distance covered and displacement may be equal
for a given movement or distance may be greater than
displacement, but the reverse is never true.
Vector & Scalar Quantities
 Scalar: Fully defined by magnitude (how much)
 Mass
 Vector: Definition requires magnitude and direction
 Force
Distance and Displacement
 Measuring change in position
 component of motion
Distance = 1/4 mile
Displacement = 0
Start and
finish
Distance and Displacement
 Another example:
 Football player (fig 2.2, p 51):
 receives kickoff at 5 yard line, 15 yards from the
left sideline
 runs it back, dodging defenders over a twisted 48
yard path, to 35 yard line, 5 yards from the left
sideline
Distance and Displacement
 Distance
 length of path traveled: 48 yards
 Displacement
 straight line distance in a specified direction
 y direction: yfinal - yinitial
 x direction: xfinal - xinitial
Distance and Displacement
 Resultant Displacement
length
of path traveled in a straight line
from initial position to final position
y
direction: yfinal - yinitial
x direction: xfinal - xinitial
R2 = (x)2 + (y)2
Components of
resultant displacement
Distance and Displacement
 Resultant Displacement
length
of path traveled in a straight line
from initial position to final position
y
direction: yfinal - yinitial
x direction: xfinal - xinitial
Components of
resultant displacement
R2 = (x)2 + (y)2
 = arctan (opposite / adjacent)
Bloomington to Chicago
Assign
x&y
coordinates
to each of
the markers
(digitize)
Speed and Velocity
 For human gait, speed is the product of stride length and
stride frequency.
 Runners traveling at a slow pace tend to increase velocity
primarily by increasing SL.

 At faster running speeds, recreational runners rely more on
increasing SF to increase velocity.
Speed and Velocity
 Most runners tend to choose a combination of stride length
and SF that minimizes the physiological cost of running.
Speed and Velocity
 The best male and female sprinters are distinguished from
their less-skilled peers by extremely high SF and short
ground contact times, although their SL are usually only
average or slightly greater than average.
Speed and Velocity
 In contrast, the fastest cross-country skiers have longer-
than-average cycle lengths, with cycle rates that are only
average.
Speed and Velocity
 Pace is the inverse of speed.
 Pace is presented as units of time divided by units of
distance (6 min/mile)
 Pace is the time taken to cover a given distance and is
commonly quantified as minutes per km or mins. per mile.
Speed and Velocity
 Acceleration - rate of change in velocity.
 Acceleration is 0 whenever velocity is constant.
 Average velocity is calculated as the final displacement
divided by the total time period.
 Instantaneous velocity - occurring over a small period of
time.
Speed and Velocity
 Measuring rate of change in position
how
fast the body is moving
 Speed
scalar
how
quantity
fast
Speed =
distance
time
meters
seconds
Examples
 Who is the faster runner:
 Michael Johnson
100m in10.09s
 200m in 19.32s (world record)
 300m in 31.56 s
 400m in 43.39s (world record)


Donovan Bailey (Maurice Greene)


50m in 5.56 s (world record)
http://www.runnersweb.com/running/fastestm.html
Instantaneous Speed
 We have calculated average speed
distance
by time to cover that distance
 Maximum speed in a race?
make
the time interval very small
 0.01 second or shorter
Speed and Velocity
 Measuring rate of change in position
how
fast the body is moving
 Speed
 Velocity
vector

quantity
how fast in a specified direction
velocity =
displacement
time
m
s
Example
 Swimmer
100
m race in 50 m pool
24s and 25s splits
 Calculate velocities & speeds
 first length, second length
 total race (lap)
Example
 Football player (fig 2.2, p 54):
 receives kickoff at 5 yard line, 15 yards from the
left sideline
 runs it back, dodging defenders over a twisted 48
yard path, to 35 yard line, 5 yards from the left
sideline
 time is 6 seconds
 Calculate velocities & speeds
 forward, side to side, resultant
Use speed to calculate time
 Running at 4 m/s
 How long to cover 2 m?
 2 m ÷ 4 m/sec= .5 sec
Quiz
If a body is traveling in the + direction and it
undergoes a – acceleration, the body will
____________________.
If a body is traveling in the – direction and it
undergoes a + acceleration, the body will
___________________.
Speed up or slow down
Acceleration
 Quantifying change of motion
 speeding up or slowing down
 rate of change of velocity
Acceleration =
 velocity
vf - vi
=

time
tf - ti
Soft landing from 60 cm
80% 1RM BP, Narrow vs Wide Grip