Ch. 2
• Scalars  quantities that have only a magnitude, no direction
Examples of scalars
→
time, distance, speed, mass, weight, work, energy, power, density, volume, temperature
• Vectors  quantities that have magnitude and direction
Examples of vectors
→
displacement, velocity, force, momentum, impulse, acceleration, torque
• Mathematical operations like addition, subtraction, multiplication work differently for Scalars and Vectors
• Distance  the total distance you travel in a certain period of time
• Displacement  the difference between your final position from your intial positioin and its direction
• Speed  the total distance you travel ÷ a certain period of time
(distance/time)
Instantaneous speed
(
S
inst
)
=
(speedometer)
lim
∆
t
→
0
∆
d
∆
t
Average speed
(
s
)
= d/t
• Velocity = (Dislpacement / Time)
Instantaneous Velocity
( V
inst
)
=
(speedometer + compass)
lim
∆
t
→
0
∆
D
∆
t
Average Velocity
(
V
)
= (Displacement/ Time)
•
(i.e.  vector ÷ scalar = vector)
S
inst
=
│
V
inst
│
│
x
│
=
means magnitude of x
S
≠
│
V
│
x
= means average of x
x = means x is a vector
• Acceleration = how fast you are changing velocity
Average acceleration
(
a
)
=
V
f
 V
i
t
Instantaneous acceleration
( a
inst
)
=
lim
∆
t
→
0
∆
v
∆
t
(derivative = d v / d t )
Example #1
You walk 10 miles West in ½ hr.. Then you rest at Starbucks for 1 hr.. Then you walk 15 miles East in
5/4 hr. Assume constant speed during each stage.
15 miles in 5/4 hr
10 miles in 1/2 hr
1 hr.
rest
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Example # 1
15 miles in 5/4 hr
1 hr. rest
10 miles in 1/2 hr
Stage 1: 10 miles in 1/2 hours
Rest for 1 hour
Stage 2: 15 miles in 5/4 hours
Assume constant speed during each stage!
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 Spring '08
 Kiledjian
 Acceleration, Energy, Mass, Power, Work, Velocity, Miles per hour, miles

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