Chapter 3: Motion in Two or Three Dimensions
3.1 Position and Velocity Vectors
•
Position vector
(
r
) – a vector that goes from the origin of the coordinate system to the point
P
=
+
+
r
xi yj zk
•
Average velocity
(
vav
) – displacement divided by the time interval
=


=
vav
r2
r1t2
t1
∆r∆t
•
Instantaneous velocity
(
v
) – instantaneous rate of change of position with time
=
→
=
v
lim∆t
0∆r∆t
drdt
o
Components of instantaneous velocity:
=
vx
dxdt
=
vy
dydt
=
vz
dzdt
3.2 The Acceleration Vector
•
Acceleration vector
(
a
) – changes in the velocity magnitude (that is, the speed)
and
changes in
the direction of velocity (that is, the direction in which the particle is moving)
•
Average acceleration
(
aav
) – the change of velocity in a given time interval
=


=
aav
v2
v1t2
t1
∆v∆t
•
Instantaneous acceleration
(
a
) – the instantaneous rate of change of velocity with time
=
→
=
a
lim∆t
0∆v∆t
dvdt
o
Components of instantaneous acceleration:
=
ax
dvxdt
=
vy
dvydt
=
vz
dvzdt
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 Spring '11
 McDemus
 Physics, Acceleration, Velocity, Nonuniform Circular Motion, acceleration vector

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