The best illustration of a uniform acceleration, is the
motion of a body near the earth's surface. In this case it
is proved by experiment that the acceleration due to the
earth is represented numerically by 981 (at Paris). Thus
a body falling to the earth has its velocity increased eacli
second by 981 centimetres per second. This does not mean
that the body describes 981 centimetres in the second, or
even describes 981 centimetres less in one second than in
the next, but that if, for instance, the body is projected
downwards with a velocity of 100 centimetres per second,
it will have at the end of the first second a velocity of 1081
centimetres per second, at the end of the second second its
velocity will be 2062 centimetres per second, and so on
during each second of the motion.
Retardation is treated as negative acceleration. If for
instance a body be projected upwards, its velocity is dimi-
nished by 981 cm. per second each second, and generally
i£f represent the retardation, our formula (ii) becomes

v=r^ft (ii)'.
If the resulting velocity should be negative it wUl de-
note that the body is moving with a certain velocity in the
direction opposite to that of projection.
PHYSICAl, tJNlTS. 3

8» To find the space described during a given time t
by a body moving with uniform acceleration, we may con-
sider that since the acceleration is uniform, the average
velocity during the interval will be the same as the velocity
at the middle of the interval, and this will clearly be V-h \ft.
