Lecture: Kinematics

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2. 2
Module Overview
Kinematics

3. 3
Acknowledgments
This presentation is based on and includes content derived from the
following OER resource:
College Physics 1
An OpenStax book used for this course may be downloaded for free at:
https://openstax.org/details/books/College-Physics

4. 4
The Study of Motion
The word kinematics is derived from a Greek term meaning motion.
Kinematics is defined as the study of motion without considering its
causes. This can be illustrated by considering a bird in flight: kinematics
describes how it turns, rises, and descends, without regard to the factors
responsible for the bird’s motion, such as the lift provided by its wings,
the effects of wind, or the force of gravity. Kinematics only describes the
bird’s motion.
Although we live in three dimensions, many situations involving motion
can be addressed in terms of one or two dimensions. For instance, a
train traveling on a long, straight railway is essentially confined to one-
dimensional motion since it can only move backwards or forwards.

5. 5
Fundamental Parameters in Kinematics
The basic parameters, or variables, that are required to describe the
motions of objects are listed below. Mathematical precision and
consistency are achieved by expressing these parameters quantitatively.
• position
• displacement
• time
• velocity
• acceleration
A change in a parameter is often represented by the Greek letter delta,
Δ. For instance, a change in time, t, is represented as Δt.

6. 6
Position Within a Reference Frame
The basis for describing an object’s motion is to specify its location at
each point in time. We locate an object by providing its position within a
reference frame.
A reference frame is usually chosen for maximum convenience in locating
a particular set of objects. Consider an airplane and its passengers. The
location of the airplane at any moment is conveniently described in terms
of its position relative to the Earth. When it comes to the passengers,
however, their positions are more conveniently given in relation to the
airplane’s cabin.

7. 7
Choosing a Reference Frame
The Earth is typically used as the
reference frame for an airplane.
On the other hand, an airplane’s
cabin provides a more convenient
reference frame for describing
the positions of its passengers.
Image: College Physics. OpenStax.

8. 8
Displacement
Displacement is defined as the change in position of an object. In
contrast, the distance that an object travels is the total length of the
path traversed between two positions. In the figure below, someone
walking from their home to the store and back again travels a distance of
6 kilometers, but upon arriving back home (the red arrow), their final
displacement is zero.
Image: College Physics. OpenStax.

9. 9
Quantifying Displacement
The change in an object’s displacement, Δx, is defined by the equation Δx
= xf − x0
In this equation, the initial position of the object is given by the quantity
x0, while the object’s final position is given by xf .
If an object moves from an initial position of 2 to a final position of 7 in a
reference frame, then its displacement is 7-2, or 5. For the reverse
situation, where the object moves from position 7 to 2, its displacement is
2-7, or -5. This illustrates that displacement has both a magnitude and
a direction.
The unit for displacement in the metric system is the meter (m).

10. 10
Scalar and Vector Quantities
A scalar is any quantity that has magnitude but no direction. A
magnitude is simply a positive or negative number (or zero). There are
many examples of parameters that are scalar quantities, including time,
speed, energy, distance, and temperature.
A vector is any quantity that has both a magnitude and a direction.
Examples of vector quantities are displacement, velocity, and
acceleration.
The direction of a vector can be indicated by an arrow. Scalars, by
contrast, lack direction and therefore are not represented by arrows.

11. 11
Coordinate Systems for One-Dimensional Motion
Motion constrained to one dimension can only occur in two directions,
such as forward or backward, right or left, up or down.
When a horizontal line is used as a one-dimensional reference frame (as
shown below), the right side is usually considered positive, while the left
side is negative.
When a vertical line is used as a one-dimensional reference frame, up is
usually considered positive, while down is negative. These are only
conventions, however, and the positive/negative directions can be
reversed if one so chooses.

12. 12
Measuring Time
Time is as fundamental to kinematics as specifying the positions of
objects. Every measurement of time involves measuring a change in
some physical parameter, such as the orientation of the hands of a
watch, or the position of the Sun in the sky. The unit for time in the
metric system is the second (s).
The elapsed time, Δt, is defined by the equation Δt = tf − t0
In this equation, the beginning time is t0 and the ending time is tf .
In many situations, it is convenient to set the beginning time to zero. In
this case (with t0 = 0), the elapsed time Δt is equal to, and
interchangeable with, the variables tf and t. In other words, when t0 = 0,
Δt = tf = t.

13. 13
Average Velocity and Speed
The average velocity of an object is defined as its displacement (Δx)
divided by the elapsed time (t) over which the displacement occurs.
(The line above the symbol v indicates an averaged value.)
The average velocity of an object is a vector quantity. Average speed is
the distance traveled divided by elapsed time, and is a scalar quantity.
The average speed is not necessarily equal to the magnitude of average
velocity.
The metric system unit for expressing velocity and speed is meters per
second, abbreviated m/s.

14. 14
Instantaneous Velocity and Speed
The instantaneous velocity (v) of an object is its velocity at a specific
instant of time. Like average velocity, the instantaneous velocity of an
object is a vector quantity.
A more formal definition of instantaneous velocity is that it is the average
velocity over an infinitesimal span of time. This more formal definition
requires the use of calculus, which is beyond the scope of algebra-based
physics.
The instantaneous speed of an object is a scalar quantity and is simply
the magnitude of its instantaneous velocity.

15. 15
Acceleration
The acceleration of a body is the change in its velocity over an elapsed
time. An object’s acceleration is produced by a change in its speed, or in its
direction, or in both.
The average acceleration of an object is defined by the equation
Instantaneous acceleration (a) is the acceleration at a specific instant.
In the metric system, acceleration is measured in units of meters per
second per second, expressed as m/s2.

16. 16
Acceleration vs. Deceleration
Acceleration may or may not be in the direction of the object’s motion.
The car at left is speeding up, which means that its acceleration is in the
same direction as its velocity. The car at right is slowing down, or
decelerating, since its acceleration is opposite its velocity.
Image: College Physics. OpenStax.

17. 17
Constant Acceleration
The acceleration of an object may change over a given timeframe, or it
may remain the same.
In many situations, the acceleration is more or less constant, remaining
the same over time. Considering motions subjected only to a constant
acceleration helps simplify the kinematic equations relating to
displacement, velocity, acceleration, and time.
A familiar example is the gravitational acceleration we all commonly
experience. When we dive into a pool, bounce on a trampoline, or
simply walk or run, the downward force of gravity we experience is
always about the same anywhere on Earth.

18. 18
1-Dimensional Equations for Constant Acceleration
When objects experience a constant acceleration, the following
kinematic equations apply to their displacement (x), velocity (v), and
acceleration (a). These equations relate to motion in a single
dimension.

19. 19
Motion of Falling Objects
All objects that fall near the surface of the Earth experience approximately
the same downward gravitational force. The average gravitational
acceleration (g) due to gravity at and near the Earth’s surface, has a widely
accepted value of g = 9.80 m/sec2.
If the effects of air resistance on an object’s motion are negligible, the
object is said to be in free fall after it is dropped.
When applying the one-dimensional equations of motion presented
previously to bodies in free fall near Earth, the constant acceleration
symbol a is replaced by g (a = g). To indicate vertical acceleration, the
displacement is denoted y instead of x.

20. 20
Graphical Analysis of Motion
Graphs depicting the parameters of motion of an object can be used to
analyze that motion.
Analyzing graphs can yield identical solutions to mathematical methods
for deriving motion equations. For instance, the slope of the line obtained
by plotting the displacement (x) of an object against the elapsed time (t)
provides the object’s velocity (v).
Similarly, the acceleration that an object experiences can be determined
from the slope of a graph of its velocity (v) vs. the elapsed time (t).

21. 21
How to Study this Module
• Read the syllabus or schedule of assignments regularly.
• Understand key terms; look up and define all unfamiliar words and
terms.
• Take notes on your readings, assigned media, and lectures.
• As appropriate, work all questions and/or problems assigned and as
many additional questions and/or problems as possible.
• Discuss topics with classmates.
• Frequently review your notes. Make flow charts and outlines from
your notes to help you study for assessments.
• Complete all course assessments.

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