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Answers to More Practice with GUSS. Answers to More Practice with GUSS. Answers to More Practice with GUSS. Answers to More Practice with GUSS. Answers to More Practice with GUSS. Answers to More Practice with GUSS. Answers to More Practice with GUSS. Answers to More Practice with GUSS. - PowerPoint PPT Presentation
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Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Answers to More Practice with GUSS
Distance, Speed and Unit Conversions: Learning Goals The student will be able to solve simple
problems involving one-dimensional average speed, distance, and elapsed time, using algebraic equations (B.2.6)
The student will be able to use and convert between different numeric representations of quantitative data. (A1.12)
SPH4C
Scalars
A scalar quantity has magnitude (size) only.
Scalars
A scalar quantity has magnitude (size) only.
Examples of scalars: distance
Scalars
A scalar quantity has magnitude (size) only.
Examples of scalars: distance speed
Scalars
A scalar quantity has magnitude (size) only.
Examples of scalars: distance speed time
Scalars
A scalar quantity has magnitude (size) only.
Examples of scalars: distance speed time work, potential and kinetic energy
Scalars
A scalar quantity has magnitude (size) only.
Examples of scalars: distance speed time work, potential and kinetic energy voltage, current, and resistance etc.
Adding Scalars: Example
Alex walks 2 m [North] and 1 m [South]. What is the total distance he walks?
Adding Scalars: Example
Alex walks 2 m [North] and 1 m [South]. What is the total distance he walks?
2 m + 1 m = 3 m
Distance is a scalar: direction doesn’t matter.
Average Speed
Average speed is defined as the distance travelled per interval of time, or
Average Speed
Average speed is defined as the distance travelled per interval of time, or
t
dvavg
Average Speed
Average speed is defined as the distance travelled per interval of time, or
Speed will therefore have units of distance over time (typically m/s).
t
dvavg
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
?
:
min75.0
180
:
avgv
Unknown
t
md
Givens
Unit conversion
But what is 0.75 minutes in seconds?
Unit conversion
But what is 0.75 minutes in seconds?
To express a measurement in different units, we multiply the measurement by a conversion factor that is equal to 1.
Unit Conversions
Since 1 minute = 60 seconds,
The unit we want to cancel out goes in the denominator of the factor.
The unit we want to get goes in the numerator.
1min1
60
s
Unit Conversions
The unit we want to cancel out goes in the denominator of the factor.
The unit we want to get goes in the numerator.
sss
451
6075.0
min1
60min75.0
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
?
:
45min1
60min75.0
180
:
avgv
Unknown
ss
t
md
Givens
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
?
:
45min1
60min75.0
180
:
avgv
Unknown
ss
t
md
Givens
s
mv
t
dv
avg
avg
45
180
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
?
:
45min1
60min75.0
180
:
avgv
Unknown
ss
t
md
Givens
sm
avg
avg
s
mv
t
dv
0.445
180
Finding Distance and Time
The equation for average speed can be rearranged to solve for distance or time:
Finding Distance and Time
The equation for average speed can be rearranged to solve for distance or time:
solved for distance
solved for timeavg
avgavg
avg
avg
avg
avg
v
dt
v
d
v
tv
dtv
tt
dtv
t
dv
Another Example
If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?
Another Example
If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?
Another Example
If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?
Another Example
If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?
?
Does it make sense that it takes someone 1.25 s to run 5 km?
skm
t
v
dt
t
dv
sm
avgavg
25.14
5
Another Example
If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?
?
:
50005
4
:
t
Unknown
mkmd
v
Givens
sm
avg
Another Example
If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?
?
:
50005
4
:
t
Unknown
mkmd
v
Givens
sm
avg
min2060
min11250
12504
5000
ss
sm
t
v
dt
t
dv
sm
avgavg
Watch for those prefixes!A metric prefix may be used to indicate a
unit that is some power of ten larger or smaller than the base unit.
Watch for those prefixes!A metric prefix may be used to indicate a
unit that is some power of ten larger or smaller than the base unit.
For example,
1 km =
Watch for those prefixes!A metric prefix may be used to indicate a
unit that is some power of ten larger or smaller than the base unit.
For example,
1 km = 1000 m or 1 × 103 m
All the Prefixes
Common Prefixes
For example, 2 s =
Common Prefixes
For example, 2 s = 2 × 10-6 s
Know how to enter this number
in your calculator :
(usually as either 2 EXP -6
or 2 EE -6
or 2 10x -6).
Common Prefixes
For example, 2 s = 2 × 10-6 s 2 ns =
Common Prefixes
For example, 2 s = 2 × 10-6 s 2 ns = 2 × 10-9 s
Common Prefixes
For example, 2 s = 2 × 10-6 s 2 ns = 2 × 10-9 s 20 ns =
Common Prefixes
For example, 2 s = 2 × 10-6 s 2 ns = 2 × 10-9 s 20 ns = 20 × 10-9 s
Multiple Conversion Factors
Finally, converting some units may require multiplying by more than one conversion factor.
Multiple Conversion Factors
Finally, converting some units may require multiplying by more than one conversion factor. For example,
s
m
s
m
s
h
km
m
h
km28
60601
11000100
6060
1
1
1000100
More Practice
Please complete “More Practice with Distance, Speed, and Unit Conversion.”