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?
2m+1m=3m
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
vavg
d

t
Average Speed
Average speed is defined as the distance
travelled per interval of time, or
vavg
d

t
Speed will therefore have units of distance
over time (typically m/s).
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?
Givens:
d  180m
t  0.75 min
Unknown:
vavg  ?
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,
60 s
1
1 min
The unit we want to cancel out goes in the
denominator of the factor.
The unit we want to get goes in the
numerator.
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.
 60 s  0.75 60
 
0.75min 
s  45 s
1
 1 min 
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
Givens:
d  180m
 60 s 
  45 s
t  0.75 min 
 1 min 
Unknown:
vavg  ?
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
Givens:
d  180m
 60 s 
  45 s
t  0.75 min 
 1 min 
Unknown:
vavg  ?
vavg
vavg
d

t
180m

45 s
Finding Speed: An Example
Matt runs 180 m in 0.75 min.
What is his average speed in m/s?
Givens:
d  180m
 60 s 
  45 s
t  0.75 min 
 1 min 
Unknown:
vavg  ?
vavg
vavg
d

t
180m

 4.0 ms
45 s
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:
d
t
 d 
vavg t  
t
 t 
vavg t  d
vavg 
vavg t
vavg
solved for distance
d

vavg
d
t 
vavg
solved for time
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?
Givens:
vavg  4 ms
d  5 km  5000m
Unknown:
t  ?
Another Example
If Megan is running at 4 m/s, how long will it
take her to run a 5 km trail?
Givens:
d
d

 t 
t
vavg
vavg  4 ms
vavg
d  5 km  5000m
5 km
t  m  1.25 s
4s
Unknown:
t  ?
Another Example
If Megan is running at 4 m/s, how long will it
take her to run a 5 km trail?
Givens:
d
d

 t 
t
vavg
vavg  4 ms
vavg
d  5 km  5000m
5 km
t  m  1.25 s
4s
Unknown:
t  ?
?
Does it make sense that it takes
someone 1.25 s to run 5 km?
Another Example
If Megan is running at 4 m/s, how long will it
take her to run a 5 km trail?
Givens:
vavg  4 ms
d  5 km  5000m
Unknown:
t  ?
vavg
d
d

 t 
t
vavg
5000m
t 
 1250s
m
4s
 1 min 
  20 min
1250s  
 60 s 
Another Example
If Megan is running at 4 m/s, how long will it
take her to run a 5 km trail?
Givens:
vavg  4 ms
d  5 km  5000m
Unknown:
t  ?
vavg
d
d

 t 
t
vavg
5000m
t 
 1250s
m
4s
 1 min 
  20 min
1250s  
 60 s 
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 ms =
Common Prefixes
For example,
 2 ms = 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 ms = 2 × 10-6 s
 2 ns =
Common Prefixes
For example,
 2 ms = 2 × 10-6 s
 2 ns = 2 × 10-9 s
Common Prefixes
For example,
 2 ms = 2 × 10-6 s
 2 ns = 2 × 10-9 s
 20 ns =
Common Prefixes
For example,
 2 ms = 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,
km  1000m   1 h  10010001 m
m
  
 
100  
 28
h  1 km   60 60s 
1 60 60 s
s
More Practice
Please complete “More Practice with
Distance, Speed, and Unit Conversion.”