### Document

```Chapter II
Mechanics
A. Streight-line motion, average and instantaneous x-
B.
C.
D.
E.
velocity
Streight-line motion with constant acceleration
Freely falling bodies
Projectile motion
Uniform Circular motion
A. Streight-line motion, average
and instantaneous x-velocity
1. Average Velocity
s = distance
r = displacement
y
t1
r1
A
s
r
r2
0
The displacement of a particle is
deﬁned as its change in position.
B
t2
x
Magnitude of Average velocity
Average Speed
 The average speed of a particle, a scalar quantity, is
deﬁned as the total distance traveled divided by the
total time it takes to travel that distance
 The average velocity of a particle is deﬁned as the
particle’s displacement r divided by the time interval
t during which that displacement occurred
2. Instantaneous Velocity
Instantaneous velocity v equals the limiting value of the
ratio r/t as t approaches zero
Magnitude of Instantaneous velocity = Instantaneous Speed
The instantaneous speed of a particle is deﬁned as the magnitude of its
velocity
3. Acceleration
The average acceleration of the particle is deﬁned as the change in velocity v
divided by the time interval t
B. Streight-line motion with constant
acceleration
C. Freely Falling Bodies
reference
h
y = -h
yo = 0
vo = 0
=-g
- h = 0 + 0 t + ½(- g) t2
-h = - ½ g t2
h = ½ g t2
For example, look exercise number 2.44 at page 87 (66)
A hot-air balloonist, rising vertically with a constant
velocity of magnitude 5.00 m/s, releases a sandbag at an
instant when the balloon is 40.0 m above the ground.
After it is released, the sandbag is in free fall. (b) How
many seconds after its release will the bag strike the
ground?
D. Projectile motion
y
vox = vo cos α
voy = vo sin α
y-direction
v = voy + at = vo sin α + at
y = voy t + ½ a t2 = vo t sin α + ½ a t2
vo
voy
0
α
vox
x-direction
v = vox = vo cos α
x = vox t = vo t cos α
x
E. Uniform Circular Motion
v2
R
v
v1
r2
r1
v2
v1
r2
r
as
r1
as = centripetal acceleration
t = time interval
```