prelecture 2 ch2 f19 velocity
TRANSCRIPT
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Lecture 2
Chapter 1 & 2
Kinematics in One Dimension
Physics I
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-i/
I like speed!! Kinematics?
–Hmm!...Not so much
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Distance/Displacement: Section 1.3
Speed/Average velocity: Section 1.4 Instantaneous velocity: Section 2.2
Average Acceleration: Section 1.5 Instantaneous Acceleration: Section 2.7
Today we are going to discuss:
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Mechanics
There are three branches of Mechanics: Kinematics Motion Forces Statics Motion Forces Dynamics Motion Forces
Kinematics describes motion of objects we are not interested in reasons (forces) of a motion
Motion
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
KinematicsNeedtodevelopavocabularyfor
describingtranslationalmotion:
PositionLevel
VelocityLevel
AccelerationLevel
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Frames of Reference
-5 5
-5
5 y-axis
x-axis
Beforestartingsolvinganyproblem,wehavetodefineacoordinatesystem(aframeofreference)todescribepositionandmotionofanobject
Inthisclass,wewillbaseproblemsinaCartesiancoordinatesystem.Wewillhave1Dand2Dproblems
Wehavefreedomtochoosedirectionofanaxis. For1dimensional(1D)motion(motioninastraightline),it’sbettertoalignthex‐axis
alongamotiondirection. Forfallingbodies,wetendtodescribepositionusingthey‐axis
origin
1 2 3 4 5
Positive direction+x
Negative direction-x
x
One dimensional (1D) problem Two dimensional (2D) problem
origin
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Distance vs. Displacement
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Distance vs. Displacement
Distance (scalar): the total path length traveled by an object
Displacement (vector): how far an object is from its starting point
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Distance vs. Displacement (1D)Distanceisascalar
Displacementisavector– Avectorhasbothmagnitudeanddirection(orsignin1‐D)
Displacement =x2- x1=+40 m
Distance =
20 40 60 70
x2
X (m)
x1
70+30 =100 m
Displacement = final position – initial position
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Distance vs. Displacement (1D)
x1 x2
Distance = 20 m
x1
Distance = 20 m
Displacement =negative
Displacement =
x1
30-10= + 20 m
x2
10-30= -20 m
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Speed and Velocity
Even Hollywood feels that there is a difference between these two terms
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Average Speed and Average Velocity
elapsed time travelleddistance
speedaverage
(Speed: Distance traveled per unit time interval)
Speed is a scalar
Velocity is a vector
(Velocity: Displacement of an object per unit time interval)
elapsed timentdisplaceme
velocityaverage
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Graphs: Average velocity
0 1 2 3 4 5 60
5
10
15
20po
sitio
n (m
)
time (s)
∆t
∆x
t1 t2
x1
x2
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Instantaneous Velocity
Average velocity does not tell the whole story…we also need:
If you watch a car’s speedometer, at any instant of time, the speedometer tells you how fast the car is going at that instant.
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Instantaneous velocity
0 1 2 3 4 5 60
5
10
15
20po
sitio
n (m
)
time (s)
t1
goes to 0
Instantaneous velocity
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Instantaneous velocity
Graphically, instantaneous velocity is the slope of the x vs t plot at a single point
Mathematically, the instantaneous velocity is the derivative of the position function
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Silly example: Finding instantaneous velocity from position (graphically)
.
>0
Turning point
Moves forwardMoves backward
0
v positive
It flies back.v4 negative
v1 (slow speed)v2 (max speed)
v3=0 (turning point)
Steeper slope ≡ higher velocityGentler slope ≡ lower velocity
A test to find a turning point: velocity changes its sign
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Finding Position from a Velocity Graph
The total displacement ∆s is called the “area under the velocity curve.” (the total area enclosed between the t-axis and the velocity curve).
The displacement is the shaded area
∆
Example
∙ Let’s integrate it: ∙ x ∙
∙
Initial position
Geometrical meaning of an integral is an area
Total displacement
displacement
v(t)
t
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Acceleration
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
AccelerationVelocity can also change with time: acceleration
elapsed time velocityof change
onacceleratiaverage
Speeding up: acceleration
Instantaneous acceleration
If we are given x(t), we can find both velocity v(t) and acceleration a(t) as a function of time
Slowing down: deceleration
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
A particle is moving in a straight line so that its position is given by the relation
x = (2 m/s2)t2 + (3 m). Calculate
(a) its average acceleration during the timeinterval from t1 = 1 s to t2 = 2 s,
(b) its instantaneous acceleration as afunction of time.
Example 2-7: Acceleration given x(t).
Example 2-7 Acceleration given x(t)
DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture2A.Danylov
Thank you