This document discusses how to calculate speed using the formula speed = distance/time. It provides examples of using the formula to calculate the speed of a bicycle, airliner, and cruise ship. It also discusses how the same process can be used to calculate other values, like density and force, that involve dividing or multiplying measurable values.

1. Math for Physical Science

2. Suppose a Corvette races down a country
road. The speedometer reads 85.
85 what?
85 miles per hour!

3. The speed of any thing can be described by
telling how far it traveled (miles) in a
certain piece of time (hour).
In the above statement, the per (in 85 miles
per hour) means “in a certain.”

4. In any mathematical expression,
whenever we see the word per,
it means to divide.
So, 85 miles per hour can be
written as 85 miles divided by
hours, or 85 .hour
miles

5. Both of these expressions mean exactly
the same thing.
Whenever we need to calculate a speed, we
divide the distance traveled by the time it took
to go that distance.
Speed = distance  time (or) speed =
time
distance

6. s stands for the speed
d stands for the distance
t stands for the time
We can use a symbol for each
word. When we do, it looks
like this:
s =
t
d

7. To calculate a speed, just follow these steps:
 Read the problem
 Find the distance given in the
problem
 Find the time given in the problem
Then:

8.  Write the math expression by itself.
 Write the expression again, but
 Write the distance (from the problem)
in place of the d
 Write the time (from the problem) in
place of the t
 Perform the division (on your calculator)
 Write the answer with the correct units
of measurement

9. Now let’s try one together.
A bicycle moves 12 miles in 2 hours. Find the speed of
the bicycle.
s = (or) s =
time
distance
t
d
In the problem, the time is 2 hours.
- We will put that in the expression for time (t).
In the problem, the distance is 12 miles.
- We will put it in the expression for distance (d).

10. We write the first two steps in our solution like this:
s =
s =
To solve, on your calculator:
Enter the top number, 12
The bar between numbers means to divide so, Press 
Enter the bottom number 2
Press = to see the answer to the division problem.
time
distance
hours2
miles12

11. My calculator gives me the answer 6! How about yours?
6 what, though?
Remember the example of the car speedometer.
The distance was given in miles and the time was given in
hours.
So, the answer is miles divided by hours or miles per hour.
S = 6
hour
miles

12. Try this one in your notebook:
An athlete runs 2 miles in 0.3 hours. What is the athlete’s
speed?
 Remember to write the math expression.
 Remember to write the measurements from the
problem in the the right places in the math
expression.
 Remember to write the answer with correct
measurement units.

13. Did
you
remember
to
write
all
3
steps?

14. Here is my solution.
s =
s =
s = 6.6666 or 6.7
t
d
hours.3
miles2
hour
miles

15. Now let’s try one with metric measures.
The math expression remains the same.
(Yeh!)
All the steps to solve remain the same. (Yeh!)
The only things that will change are the units
of measure.
The Problem:
An airliner flies 400 meters in 50 seconds.
What is the speed of the airliner?

16. The Solution:
s =
s =
s = 8
t
d
seconds50
meters400
second
meters

17. Please try this one in your notebook:
A cruise ship travels 3000 meters in 250 seconds. What is
its speed?

18. My solution looks like this:
s =
s =
s = 12
t
d
seconds250
meters3000
second
meters

19. This same set of steps works for any math expression to
solve any kind of problem.
For instance, the density of a material is given by the
expression:
density = (or), in symbols, d =
volume
mass
V
m
A density problem to try:
A block has a mass of 500 grams and a volume of 20 cubic
centimeters. What is the density of the block?

20. The solution looks like this:
d =
d =
d = 20
V
m
scentimetercubic25
grams500
centimetercubic
grams

21. Other types of problems, and the math expressions used to
solve them, use other math operations besides division.
The force on an object can be found by multiplying the
force times the acceleration:
Force = mass acceleration (or) F = m a 
s
m/s
This problem will illustrate:
A bowling ball has a mass of 8 kg. If I drop one from the
roof of the school, Earth’s gravity accelerates the bowling
ball at 10 . How much force accelerates the bowling ball?

22. My solution is:
F = m a
F = 8 kg 10
F = 80 Newtons
(Note: Newton is the metric unit of force. When we
multiply mass in kg by acceleration in , the answer
comes out in Newtons.)


s
m/s
s
m/s

23. Please see the teacher for a problem practice sheet.
Remember:
You may write math expressions in words or in symbols.
In your work, please remember to show all the steps I have
shown in each of the sample problems.
Remember that the values you put in the math expressions
are measurements, so they MUST include correct
measurement units.