The formula for the speed of a moving object is where is the distance covered, and is the time taken.
For example, if a car travels a distance of within a time of at constant speed, then we can find the speed of the car using the formula as follows:
But what is the unit of speed? We can find it by substituting the units for distance and time into the formula:
So, the speed of the car is When the unit has a quotient like this, we say "meters per second."
The gravitational acceleration of a body in free fall is given by the formula where is the distance, measured in meters, traveled by the body due to gravity in time measured in seconds. Determine an appropriate measurement unit for gravitational acceleration.
To find the unit of gravitational acceleration, we substitute the given units of distance and time into the formula:
Therefore the appropriate unit is Here, we ignore the unitless constant since it does not affect the units.
The momentum $p$ is related to mass $m$ and velocity $v$ by the equation $p = m v.$ If $m$ is measured in kilograms and $v$ is measured in $\dfrac{\textrm{m}}{\textrm{s}}$, what is an appropriate measurement unit for momentum?
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a
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$\dfrac{\textrm{m}}{\textrm{kg}}$ |
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b
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$\dfrac{\textrm{s}}{\textrm{kg} \, \textrm{m}}$ |
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c
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$\dfrac{\textrm{kg} \, \textrm{m}}{\textrm{s}}$ |
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d
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$\dfrac{\textrm{kg}}{\textrm{s}}$ |
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e
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$\dfrac{\textrm{kg} \, \textrm{m}}{\textrm{s}^2}$ |
The velocity of a body with uniform linear motion is given by the formula $v = \dfrac{d}{t},$ where $d$ is the distance traveled by the body in kilometers and $t$ is the time passed in hours.
Determine an appropriate measurement unit for velocity.
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a
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$\dfrac{\textrm{km}^2}{\textrm{hour}}$ |
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b
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$\dfrac{\textrm{km}}{\textrm{hour}}$ |
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c
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$\dfrac{\textrm{hour}^2}{\textrm{km}^2}$ |
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d
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$\dfrac{\textrm{km}^2}{\textrm{hour}^2}$ |
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e
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$\dfrac{\textrm{km}}{\textrm{hour}^2}$ |
The frequency of a wave is given by the formula where represents the velocity of the wave in while represents the length of the wave in meters. Find an appropriate measurement unit for frequency.
We can find the unit of frequency by substituting the given units of velocity and length into the formula and simplifying.
Thus, the unit of frequency is
The pressure $P$ applied to a surface is related to the magnitude of the normal force $F$ and the area $A$ of the surface on contact by the equation $P=\dfrac{F}{A}.$ If $F$ is measured in Newtons $\left(\dfrac{\textrm{kg} \, \textrm{m}}{\textrm{s}^2}\right)$, and $A$ is measured in square meters, determine an appropriate measurement unit for pressure.
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a
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$\dfrac{\textrm{s}^2}{\textrm{kg} \, \textrm{m}}$ |
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b
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$\dfrac{\textrm{s}^2 \, \textrm{m}}{\textrm{kg}}$ |
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c
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$\dfrac{\textrm{kg} \, \textrm{s}^2}{m}$ |
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d
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$\dfrac{\textrm{kg} \, \textrm{m}}{\textrm{s}^2}$ |
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e
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$\dfrac{\textrm{kg}}{\textrm{m} \, \textrm{s}^2}$ |
The period of a wave is given by the formula $ p = \dfrac{l}{v}, $ where $l$ represents the length of the wave in meters, and $v$ represents the velocity of the wave in $\dfrac{\textrm{m}}{\textrm{s}}.$ Find an appropriate measurement unit for period.
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a
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$\dfrac{1}{\textrm{s}}$ |
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b
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$\dfrac{\textrm{s}}{\textrm{m}^2}$ |
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c
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$\textrm{m}$ |
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d
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$\textrm{s}$ |
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e
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$\dfrac{\textrm{m}^2}{\textrm{s}}$ |
Sometimes, we can be given a formula with values whose units are not the standard ones we know.
For instance, suppose the formula for a person's popularity is given by where is the number of friends that person has, and is the number of siblings they have.
If we want to find the unit of popularity, then we need to substitute the units for the number of friends () and the number of siblings () into the formula.
The units for the number of friends is '' since we say 'I have friends'.
Similarly, the units for the number of siblings is ''
Substituting these units into the formula, we get
Therefore the appropriate unit is , or "friends per sibling." Here we ignore the constant since it does not affect the units.
A farm with chickens produces eggs per year. To determine the number of eggs produced by one chicken on average, the farmer uses the formula where is the number of eggs produced by the farm during the year, and is the number of chickens on the farm.
In words, what is the appropriate measurement unit for
We are solving for measurement units, so we can ignore the quantities and They do not matter if we are just solving for units.
Since represents and represents the appropriate measurement unit for is In words, this is "eggs per chicken."
$15$ children eat $400$ cookies monthly. If we want to determine the number of cookies that each child eats on average, we use the formula $A = \dfrac{n}{c},$ where $n$ represents the total of cookies while $c$ represents the total of children.
Find an appropriate measurement unit for $A.$
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a
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$\dfrac{\textrm{children}}{\textrm{cookie}}$ |
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b
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$\dfrac{\textrm{cookies}}{\textrm{child}^2}$ |
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c
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$\dfrac{\textrm{children}}{\textrm{cookie}^2}$ |
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d
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$\dfrac{\textrm{cookies}^3}{\textrm{child}^2}$ |
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e
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$\dfrac{\textrm{cookies}}{\textrm{child}}$ |
In a dog kennel, $20$ dogs eat $60$ treats each day. If we want to determine the number of treats that each dog eats on average, we use the formula $A = \dfrac{n}{d},$ where $n$ represents the total of treats while $d$ represents the total number of dogs.
Find an appropriate measurement unit for $A.$
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a
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$\dfrac{\textrm{treats}}{\textrm{dog}^2}$ |
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b
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$\dfrac{\textrm{treats}}{\textrm{dog}}$ |
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c
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$\dfrac{\textrm{dogs}}{\textrm{treat}^2}$ |
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d
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$\dfrac{\textrm{treats}^2}{\textrm{dog}^2}$ |
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e
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$\dfrac{\textrm{dogs}}{\textrm{treat}}$ |