Kinematics The study of how objects move The study of how objects move
Jan 06, 2018
KinematicsThe study of how objects The study of how objects
movemove
Where are You?
We must start with a
question
PositionReference Point:
Zero location in a coordinate system or frame.
Frame of Reference:
Coordinate system used to define motion.
Position: Separation between an object and a reference point. It needs a distance and direction.
i.e. 3.0 meters to the right.
To find where you are you need the following:
You are Here
You are Here
You are Here
You are Here
You are Here
You are Here
You are Here
You are Here
Distance vs. Displacement
Distance is simply the total path length traversed in moving from one location to another
Distance is a SCALAR quantity. A measurement with only magnitude, or size.
50 m
Distance vs. Displacement
Displacement is the straight-line distance between two points, along with the direction from the starting point to the final position.
Displacement is a VECTOR quantity. A measurement with magnitude, or size and a direction
10 m East
Difference between Distance and Displacement
Walking to
Physics Lab
Distance = 8 mDisplacement = 8m right
Right - PositiveLeft - Negative
Direction Convention :Displacement =+8m
Speed
SpeedTime
Distance
Speed is the rate at which distance is traveled.
=10 m/s
20 m
2 sec
Speed m
202sec
Speed is a scalar
quanity
Average speedAverage speed is the distance d traveled, the actual path, divided by the total time t elapsed in traveling that distance.
Average Speed Distance TraveledTotal Time
Instantaneous SpeedInstantaneous Speed is how fast an object is moving at a
particular instant of time.
Average vs. Instantaneous Speed
Velocity
V xt
x xt t
o
o
xo
to
VelocityVelocity tells how fast something is moving and in what direction. Velocity is a vector quantity.Average VelocityAverage Velocity is the
displacement divided by the total travel time =initial position,
commonly zero
= initial time, commonly zero
V xt
When xo and to are zero
A jogger jogs from one end to the other of a straight 300 meter track (from point A to point B) in 2.50 min and then turns around and jogs 100 m back toward the starting point (to point C) in another 1.00 min. What are the jogger’s average speeds and velocities in going
A) From A to BB) From A to C after turning around
Speed and
Velocity Problem
avg speed dt
ms
ms
300150
2 00.
v xt
ms
B
B
ms
300150
2 00.
A)
v x xt t
m ms sc
B C
B C
ms
300 100150 60 0
0 952( ).
.
Given:xB = 300m - 0m = +300m (from A to B)xC = 200m – 300m = -100m (from B to C)tB = 2.50 min = 150 stC = 1.00 min = 60.0 s
B)
Average speed and velocity from A to B
Average speed and velocity from A to Cavg speed
dt
m ms s
ms
300 100150 60 0
190.
.
Two Compone
nts of Velocity
GraphicGraphical look al look
at at MotionMotion
AcceleratioAccelerationnPosition is the separation between
an object and a reference point. Displacement is a change in positionVelocity is the time rate change of displacementAcceleration is the time rate change of velocityAll four are vector quantitiesRepresented by a magnitude and direction
Kinematic Equations
v dt
d dt t
2 1
2 1
d dt
2 1
a vt
v vt t
2 1
2 1
v vt
2 1
v v at2 1
accelerationacceleration
velocityvelocity
v dt
v v v
1 2
2
dt
v v1 2
2With a constant acceleration
Total Displacement and total time
Average Velocityd v v t 1
2 1 2( )
d v v t 12 1 2( ) v v at2 1 v at1
d v v at t 12 1 1( ( ))
d v t at 12 1
12
22( )
d v t at 11
22
d v v t 12 1 2( )
v v ad22
12 2
d v va
2
212
2d v v v va
1 2 2 1
2
t v va
2 1
d vt
v v at2 1 v v1 2
2v v v
1 2
2 v va
2 1
Kinematic Equations
v dt
v v at2 1
a vt
d v t at 11
22
v v ad22
12 2
Problem:
Ally the Alligator takes off from an airfield. She starts from rest and obtains a velocity of 36 m/s at take off in 20.0 seconds.
What is her acceleration down the runway?
How far did she go down the runway?a vt
v vt
2 136 0
20
ms
ms
sec18 2. m
s
18 2. ms
d v v t 12 1 2( )d m
sms 1
2 0 36 20 0( ) . secd m360