SPH3U: Physics Math Part C and D
PART C: Create the Scientific Unit
Most quantities that we measure in physics, such as length, mass, or time, require units to be meaningful. We use SI
(Systeme International = metric system) base units of metres (m), kilograms (kg) and seconds (s) to specify these
quantities, but we also use these base units to create new scientific units to describe other quantities.
Example:
To create the SI unit for volume, we use the definition of volume: volume = length × width × height. The SI base unit
for length (and width and height) is metres (m), so the unit of volume is (m)×(m)×(m) = m3 (metres cubed, or cubic
metres).
1. speed (or velocity) = (distance traveled/total time)
2. acceleration = (velocity/time)
3. density = (mass/volume)
4. force = (mass × acceleration)
5. pressure = (force/area)
6. work = (force × distance)
7. gravitational potential energy = (mass × acceleration × height)
Note: It is not necessary to memorize these new units! You should always be able to derive the units if you have the
equation!
PART D: Formulas and Unit Analysis
You will be introduced to many mathematical formulas this year, formulas that describe some kind of behavior or
phenomenon in the physical world. When we are first introduced to a formula, it is more important to see if it “makes
sense” than to memorize it. One way that we can do this is to examine the units of the formula – sometimes the units
make intuitive sense because they correspond to our personal experience, and sometimes we can deduce from the
units that the equation has been written down incorrectly.
Example:
Consider the formula for speed: 𝑣 =
∆𝑑
.
∆𝑡
Look at the right hand side of the “equals” sign. The triangles Δ are the Greek letter “delta” which mean “a change in”
in physics or math, but don’t worry too much about that right now. The variable “d”, you may be able to guess, means
“distance moved” or “distance traveled” which has units of metres (m), and the variable “t” stands for “time” with
units of seconds (s). So speed v (left hand side of the equation) must have units of metres per second (m/s). You are
familiar with car speedometers measuring “km/h”, which also expresses units of distance divided by time, and which
can be easily converted to m/s. So this formula for speed appears to be correct (in terms of units) and makes physics
sense.
1. In grade 12 physics, you will learn the equation for momentum: 𝑚𝑣 = 𝐹𝑡, where m is mass, v is speed, F is
force, and t is time. What are the units of each side of the equation? (For force, refer back to your answer for
Part C #4 above). Is the equation likely correct? (i.e. are the units on both sides of the equation the same =
dimensionally correct?)
1
2. Given the formula ∆𝑑 = 𝑣1 𝑡 + 2 𝑎𝑡 2 , where Δd is the displacement (or distance traveled), t is the time, v1 is
the initial speed, and a is acceleration, what are the units of each side of the equation? (Extra info: constants –
like ½ - do not have units) Is the equation dimensionally correct?
3. Given the formula (𝑓2 )2 =
𝑓1 𝑣𝑠
,
𝑣𝑠 +𝑣𝑜
where f1 and f2 are frequencies (measured in units of Hertz, Hz), and vs and
vo are speeds, what are the units of each side of the equation? Is the equation dimensionally correct?
Physics Math Assignment
Answers:
PART C:
6.
1. m/s
kg  m 2
kg  m
×
m
=
s2
s2
kg  m 2
kg × m/s2 × m =
(same units as #6)
s2
2. m/s2
7.
3. kg/m3
PART D:
kg  m
4. kg × m/s2, or
(you will learn that this is
s2
also called a Newton, N)
5.
kg  m
2
 m =
s2
𝑘𝑔∙𝑚
𝑠 2 𝑚2
=
𝑘𝑔
𝑠2𝑚
𝑜𝑟
𝑘𝑔
𝑚𝑠 2
1. YES, 𝐿𝐻𝑆 = 𝑘𝑔
𝑚
𝑠
, 𝑅𝐻𝑆 = 𝑘𝑔
2. YES, 𝐿𝐻𝑆 = 𝑚, 𝑅𝐻𝑆 =
𝑚
𝑚
𝑠
𝑠+
3. NO, 𝐿𝐻𝑆 = (𝐻𝑧)2 , 𝑅𝐻𝑆 = 𝐻𝑧
𝑚
𝑠2
𝑚
𝑠2
𝑠 = 𝑘𝑔
2
𝑚
𝑠
𝑠 =𝑚+𝑚=