you are located, no matter what the gravity, your duplicate will have
exactly the same mass as THE kilogram back in France. Problem solved.
You might think the position of an object is an easy property to measure,
but where exactly do you measure its position from? For example, if you
wanted to specify your body’s position in space, from where would you
take the measurement? Would it be from your feet, your stomach, or your
head? This presents a problem because there would be a big discrepancy
between the position of your head and that of your feet.
Physicists solve this problem by taking the location of the center of
mass of the object as its position. The center of mass is the object’s balance
point. This would be the place where you could attach an imaginary piece
of string to the object and it would balance in any position. Another good
way of thinking about the center of mass is that it is the average location of
all the mass in a body.
Velocity is a vector quantity (a quantity that has magnitude and direction)
that expresses the rate of change of distance over time. The standard unit of
measurement of velocity is meters per second, abbreviated to m/s. This can
be expressed mathematically as:
The Greek capital letter D, read as delta, is used in mathematics to denote a
change in quantity. Therefore, Dt in equation (1.75) represents a change in
time (a time interval) and Dx a change in distance (a displacement). D is
calculated as the after quantity minus the before quantity. Therefore if an
object’s position att=0is2(before) and att=1is5(after), Dx is5–2=
3. This can also result in negative values. For instance if an object’s posi
tion att=0is7(before) and att=1is3(after), Dx is3–7=–4.
NOTE Delta’s little brother, the lowercase letter delta, written as d, is used to
represent very small changes. You often see d used in calculus. Because d looks
similar to the letter d, to prevent confusion, mathematicians tend to avoid using
d to represent distance or displacement in their equations. Instead, a less
ambiguous symbol such as Dx is used.
Using equation (1.75), it’s easy to calculate the average velocity of an
object. Let’s say you want to work out the average velocity of a ball as it
rolls between two points. First calculate the displacement between the two
points, then divide by the amount of time it takes the ball to cover that
30 | Chapter 1