velocity per unit time—as av/t. In
this equation, ais acceleration, vis
change in velocity of an object (the delta
symbol stands for change), and tis the
change in time needed to reach the veloc-
ity. For example, if acceleration is con-
stant, and a person drove from a standing
point to 60 miles per hour in 5 seconds,
the equation becomes: 60 miles per hour /
5 seconds (or final speed minus the initial
speed, all divided by the elapsed time).
This means that the acceleration is equal
to 17.6 feet per second squared (you have
to change the miles per hours to feet and
seconds, respectively).
Momentum relates to the amount of
energy maintained by a moving object; it
is also defined as the force necessary to
stop an object from moving. It depends
on the mass and velocity of an object, and
is represented as: Mmv, in which Mis
momentum, mis the mass of the object,
and vis the object’s velocity.
What is the mathematical distinctionbetween weightand mass?
There is a definite difference between weight and mass, which is easily represented in
the formula Wmg, in which Wis weight (or the gravitational pull on an object), mis
mass (or the quantity of matter in an object), and gis the gravitational pull. For exam-
ple, if you wanted to lose weight, you could move further from the Earth or live on the
Moon (in both cases, the gravitational pull would be less). But remember, no matter
where you travel in the universe, you will always have the same mass—unless you diet!
Can Newton’s three lawsbe expressed mathematically?
Yes, Newton’s three laws are all based on mathematical formulas, but the equations
would be too complex for this text. They are defined (some with applicable mathemati-
cal notation) as follows: Newton’s First Law (Law of Inertia)states that without any
forces acting on an object, it will maintain a constant velocity. In other words, an
object will stay still or keep moving in a straight line until something pushes it to
change its speed or direction. The one force that stops almost everything from stand-
ing completely still or moving in a straight line is gravity. This is easily seen when you 277
MATH IN THE PHYSICAL SCIENCES
Whether you are standing on the Moon or on Earth,
your masswill always be the same; however, you will
weighless on the Moon because the gravitational
pull on your body is less. Taxi/Getty Images.