<< Chapter < Page Chapter >> Page >
Negative vector is a relative term - not an independent concept. We completely loose the significance of a negative vector when we consider it in isolation. A negative vector assumes meaning only in relation with another vector or some reference direction.

Acceleration and deceleration are terms which are generally considered to have opposite meaning. However, there is difference between literal and scientific meanings of these terms. In literal sense, acceleration is considered to describe an increase or positive change of speed or velocity. On the other hand, deceleration is considered to describe a decrease or negative change of speed or velocity. Both these descriptions are incorrect in physics. We need to form accurate and exact meaning of these two terms. In this module, we shall explore these terms in the context of general properties of vector and scalar quantities.

A total of six (6) attributes viz time, distance, displacement, speed, velocity and acceleration are used to describe motion. Three of these namely time, distance and speed are scalar quantities, whereas the remaining three attributes namely displacement, velocity and acceleration are vectors. Interpretations of these two groups are different with respect to (ii) negative and positive sign and (i) sense of increase and decrease. Further these interpretations are also affected by whether we consider these terms in one or two/three dimensional motion.

The meaning of scalar quantities is more and less clear. The scalar attributes have only magnitude and no sense of direction. The attributes “distance” and “speed” are positive quantities. There is no possibility of negative values for these two quantities. In general, time is also positive. However, it can be assigned negative value to represent a time instant that occurs before the start of observation. For this reason, it is entirely possible that we may get negative time as solution of kinematics consideration.

Negative vector quantities

A vector like acceleration may be directed in any direction in three dimensional space, which is defined by the reference coordinate system. Now, why should we call vector (as shown in the figure below) represented by line (i) positive and that by line (ii) negative? What is the qualification for a vector being positive or negative? There is none. Hence, in pure mathematical sense, a negative vector can not be identified by itself.

Vector representation in three dimensional reference

Vectors in isolation have no sense of being negative.

In terms of component vectors, let us represent two accelerations a 1 and a 2 as :

a 1 = - 2 i + 3 j - 4 k a 2 = - 2 i +- 3 j + 4 k

Why should we call one of the above vectors as positive and other as negative acceleration? Which sign should be considered to identify a positive or negative vector? Further, the negative of a 1 expressed in component form is another vector given by - a 1 :

- a 1 = - ( - 2 i + 3 j - 4 k ) = 2 i - 3 j + 4 k

So, what is the actual position? The concept of negative vector is essentially a relative concept. If we represent a vector A as shown in the figure below, then negative to this vector – A is just another vector, which is directed in the opposite direction to that of vector A and has equal magnitude as that of A .

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask