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  • Define and distinguish between scalar and vector quantities.
  • Assign a coordinate system for a scenario involving one-dimensional motion.
A small jet airplane flying toward the left.
The motion of this Eclipse Concept jet can be described in terms of the distance it has traveled (a scalar quantity) or its displacement in a specific direction (a vector quantity). In order to specify the direction of motion, its displacement must be described based on a coordinate system. In this case, it may be convenient to choose motion toward the left as positive motion (it is the forward direction for the plane), although in many cases, the x size 12{x} {} -coordinate runs from left to right, with motion to the right as positive and motion to the left as negative. (credit: Armchair Aviator, Flickr)

What is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector    is any quantity with both magnitude and direction . Other examples of vectors include a velocity of 90 km/h east and a force of 500 newtons straight down.

The direction of a vector in one-dimensional motion is given simply by a plus ( + ) size 12{ \( + \) } {} or minus ( ) size 12{ \( - \) } {} sign. Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector’s magnitude (e.g., the larger the magnitude, the longer the length of the vector) and points in the same direction as the vector.

Some physical quantities, like distance, either have no direction or none is specified. A scalar    is any quantity that has a magnitude, but no direction. For example, a 20ºC temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km/h speed limit, a person’s 1.8 m height, and a distance of 2.0 m are all scalars—quantities with no specified direction. Note, however, that a scalar can be negative, such as a 20ºC temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented by arrows.

Coordinate systems for one-dimensional motion

In order to describe the direction of a vector quantity, you must designate a coordinate system within the reference frame. For one-dimensional motion, this is a simple coordinate system consisting of a one-dimensional coordinate line. In general, when describing horizontal motion, motion to the right is usually considered positive, and motion to the left is considered negative. With vertical motion, motion up is usually positive and motion down is negative. In some cases, however, as with the jet in [link] , it can be more convenient to switch the positive and negative directions. For example, if you are analyzing the motion of falling objects, it can be useful to define downwards as the positive direction. If people in a race are running to the left, it is useful to define left as the positive direction. It does not matter as long as the system is clear and consistent. Once you assign a positive direction and start solving a problem, you cannot change it.

An x y coordinate system. An arrow pointing toward the right shows the positive x direction. Negative x is toward the left. An arrow pointing up shows the positive y direction. Negative y points downward.
It is usually convenient to consider motion upward or to the right as positive ( + ) size 12{ \( + \) } {} and motion downward or to the left as negative ( ) .

A person’s speed can stay the same as he or she rounds a corner and changes direction. Given this information, is speed a scalar or a vector quantity? Explain.

Speed is a scalar quantity. It does not change at all with direction changes; therefore, it has magnitude only. If it were a vector quantity, it would change as direction changes (even if its magnitude remained constant).

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Section summary

  • A vector is any quantity that has magnitude and direction.
  • A scalar is any quantity that has magnitude but no direction.
  • Displacement and velocity are vectors, whereas distance and speed are scalars.
  • In one-dimensional motion, direction is specified by a plus or minus sign to signify left or right, up or down, and the like.

Conceptual questions

A student writes, “ A bird that is diving for prey has a speed of 10 m / s size 12{ - "10"m/s} {} .” What is wrong with the student’s statement? What has the student actually described? Explain.

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What is the speed of the bird in [link] ?

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Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.

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A weather forecast states that the temperature is predicted to be 5ºC the following day. Is this temperature a vector or a scalar quantity? Explain.

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Questions & Answers

An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
MAHADEV
sorry..E and R are non zero...
MAHADEV
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
Elene Reply
what Is linear momentum
Victoria Reply
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Blessing Reply
where
Fayyaz
Myanmar
Pyae
hi
Iroko
hello
Abdu
Describe an experiment to determine short half life
Tyson Reply
what is science
Kenedy Reply
it's a natural phenomena
Hassan
sap
Emmanuel
please can someone help me with explanations of wave
Benedine
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
what is physics
Caya Reply
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
Magret Reply
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
Ekwunazor Reply
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
Lathan Reply
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
what is wave
Ochigbo Reply
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
Lord Reply
yeah that was a mistake
Lord
if it flows in three dimensions does it mean if an object theoretically moves beyond the speed of light it won't experience time
Lord
but if an object moves beyond the speed of light time stops right for it
Lord
yes but at light speed it ceases
Lord
yes it always flow from past to future.
Noman
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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