Page 46 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 3

Motion in a

Straight Line

VELOCITY

The velocity of a body is a vector quantity that describes both how fast it is moving and the direction in which it
is headed. The magnitude of a velocity is sometimes called speed.
In the case of a body traveling in a straight line, the magnitude of its velocity is simply the rate at which it
covers distance. The average velocity ¯v of such a body when it covers the distance s in the time t is
s
¯ v =
t
distance
Average velocity =
time
The average velocity of a body during the time t does not completely describe its motion, however, because
during the time t it may sometimes have gone faster than ¯v and sometimes slower. The velocity of a body at any
given moment is called its instantaneous velocity and is given by
s
v inst =
t
Here s is the distance the body has gone in the very short time interval t at the specified moment. ( is the
capital Greek letter delta and is often used to indicate a small change in some quantity.) Instantaneous velocity
is what a car’s speedometer indicates.
When the instantaneous velocity of a body does not change, it is moving at constantvelocity. For the case of
constant velocity, the basic formula v = s/t can be rewritten to give the distance covered in a given period of time:

s = vt
Distance = (constant velocity)(time)

Another way to write v = s/t gives the time needed to cover a given distance at the constant velocity v:
s
t =
v
distance
Time =
constant velocity
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