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)

Scalars

A scalar quantity has magnitude (size) only.

Scalars


Examples of scalars: distance

Scalars


Examples of scalars: distance speed

Scalars


Examples of scalars: distance speed time

Scalars


Examples of scalars: distance speed time work, potential and kinetic energy

Scalars


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


t

dvavg

Average Speed


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?




?

:

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




?

:

45min1

60min75.0

180

:

avgv

Unknown

ss

t

md

Givens




?

:

45min1

60min75.0

180

:

avgv

Unknown

ss

t

md

Givens

s

mv

t

dv

avg

avg

45

180




?

:

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


?

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


?

:

50005

4

:

t

Unknown

mkmd

v

Givens

sm

avg

Another Example


?

:

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.



For example,

1 km =



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.”

Answers to More Practice with GUSS.

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