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dicular to your velocity vector. A useful definition of an acceleration vector
should relate in a systematic way to the actual physical effects produced by
the acceleration, so a physically reasonable definition of the acceleration
vector must allow for cases where it is not in the same direction as the
motion.
Self-Check
In projectile motion, what direction does the acceleration vector have.
The following are two examples of force, velocity, and acceleration
vectors in complex motion.
As we have already seen, the projectile has a
x
=0 and a
y
=-g,
so the acceleration vector is pointing straight down.
a
b
c
e
d
.
v
points
down
.
v
points
up
.
v
˜
0
a
b
c
d
e
The downward force
of gravity produces
a downward accel-
eration vector.
The upward force from
the ground is greater than
the downward force of
gravity. The total force on
the horse is upward, giving
an upward acceleration.
This figure shows outlines traced
from the first, third, fifth, seventh, and
ninth frames in Muybridge’s series of
photographs of the galloping horse.
The estimated location of the horse’s
center of mass is shown with a circle,
which bobs above and below the hori-
zontal dashed line.
If we don’t care about calculating ve-
locities and accelerations in any par-
ticular system of units, then we can
pretend that the time between frames
is one unit. The horse’s velocity vec-
tor as it moves from one point to the
next can then be found simply by
drawing an arrow to connect one po-
sition of the center of mass to the next.
This produces a series of velocity vec-
tors which alternate between pointing
above and below horizontal.
The
.
v vector is the vector which
we would have to add onto one veloc-
ity vector in order to get the next ve-
locity vector in the series. The
.
v vec-
tor alternates between pointing down
(around the time when the horse is in
the air, b) and up (around the time
when the horse has two feet on the
ground, d).
Chapter 8Vectors and Motion