PHYSICS
PHYS 301
Automotive Engineering
Technology- Part 2
Kinematics:
Motion in One Dimension
Types of motion
Motion in three
dimension
Motion in two
dimension
Motion in one
dimension
1- Motion in one dimension
x
a
x1
x2
b
X
Y
2-Motion in two dimension
b
In this case the vector has two
components
like
circular
and
projectile motion
a
X
Y
3- Motion in three dimension
X
Z
2.1 Displacement & Velocity
Learning Objectives
• Describe motion in terms of displacement, time,
and velocity
• Calculate the displacement of an object traveling
at a known velocity for a specific time interval
• Construct and interpret graphs of position versus
time
Essential Concepts
• Frames of reference
• Vector vs. scalar quantities
• Displacement
• Velocity
–Average velocity
–Instantaneous velocity
• Acceleration
• Graphical representation of motion
Reference Frames
• Motion is relative
• When we say an object is moving, we mean it is
moving relative to something else (reference frame)
Scalar Quantities & Vector
Quantities
•
•
•
•
Scalar quantities have magnitude
Example: speed
15 m/s
Vector quantities have magnitude and direction
Example: velocity
15 m/s North
Displacement
•
Displacement vs. Distance
• Distance is the length of the path that an object
travels
• Displacement is the change in position of an object
Determining Displacement
In these examples, position is determined with
respect to the origin, displacement wrt x1
http://www.sfu.ca/phys/100/lectures/lecture5/lecture5.html
Indicating Direction of Displacement
Direction can be indicated by sign, degrees, or
geographical directions.
When sign is used, it follows the conventions of a
standard graph
Positive
Right
Up
Negative
Left
Down
Reference Frames &
Displacement
• Direction is relative to the initial position, x1
• x1 is the reference point
Average Velocity
Speed: how far an object travels in a given time interval
Velocity includes directional information:
Average Velocity
displacement
average velocity =
time interval
Dx x f - xi
v=
=
Dt
t
Velocity
Average velocity compared to
instantaneous velocity
Instantaneous velocity is the slope of the tangent
line at any particular point in time.
Instantaneous Velocity
• The velocity at a given moment in time
• The instantaneous velocity is the velocity, as Δt
becomes infinitesimally short,
• i.e. limit as Δt 0
2.2 Acceleration
Learning Objectives
• Describe motion in terms of changing velocity
• Compare graphical representations of accelerated and nonaccelerated motions
• Apply kinematic equations to calculate distance, time, or
velocity under conditions of constant acceleration
x-t graph when velocity is changing
Acceleration
Acceleration is the rate of change of velocity.
Acceleration: Change in Velocity
•
•
•
•
Acceleration is the rate of change of velocity
a = ∆v/∆t
a = (vf – vi) / (tf – ti)
Since velocity is a vector quantity, velocity can change in magnitude
or direction
• Acceleration occurs whenever there is a change in magnitude or
direction of movement.
Negative Acceleration
• Both velocity & acceleration can have (+) and (-) values
• Negative acceleration does not always mean an object is
slowing down
Velocity-Time Graphs
• Is this object accelerating?
• How do you know?
• What can you say about its motion?
www.gcsescience.com
Velocity-Time Graph
• Is this object accelerating?
• How do you know?
• What can you say about its motion?
• What feature of the graph represents acceleration?
www.gcsescience.com
Motion with constant accelertion
•
15 m / s
Exercise
•
Exercise
•
2.3 Falling Objects
Objectives
1. Relate the motion of a freely falling body to motion with
constant acceleration.
2. Calculate displacement, velocity, and time at various points
in the motion of a freely falling object.
3. Compare the motions of different objects in free fall.
Motion Graphs of Free Fall
What do motion graphs of an object in
free fall look like?
Free Fall
• In the absence of air resistance, all objects fall to earth with a
constant acceleration
• The rate of fall is independent of mass
• In a vacuum, heavy objects and light objects fall at the same
rate.
• The acceleration of a free-falling object is the acceleration of
gravity, g
• g = 9.81m/s2
memorize this value!
Free Fall
• Free fall is the motion of a body when
only the force due to gravity is acting on
the body.
• The acceleration on an object in free fall
is called the acceleration due to
gravity, or free-fall acceleration.
• Free-fall acceleration is denoted with by
ag (generally) or g (on Earth’s surface).
Free Fall Acceleration
• Free-fall acceleration is the same for all
objects, regardless of mass.
• This book will use the value g = 9.81 m/s2.
• Free-fall acceleration on Earth’s surface is –
9.81 m/s2 at all points in the object’s motion.
• Consider a ball thrown up into the air.
– Moving upward: velocity is decreasing,
acceleration is –9.81 m/s2
– Top of path: velocity is zero, acceleration is –9.81
m/s2
– Moving downward: velocity is increasing,
acceleration is –9.81 m/s2
Sample Problem
• Falling Object
• A player hits a volleyball so that it
moves with an initial velocity of 6.0
m/s straight upward.
• If the volleyball starts from 2.0 m
above the floor,
• how long will it be in the air before it
strikes the floor?