Math for Physical Science

Suppose a Corvette races down a country road. The speedometer reads 85.

85 what?

85 miles per hour!

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.”

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

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

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

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:

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

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).

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

hours 2

miles 12

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

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.

Did

you

remember

to

write

all

3 steps?

Here is my solution.

s =

s =

s = 6.6666 or 6.7

t

d

hours .3

miles 2

hour

miles

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?

The Solution:

s =

s =

s = 8

t

d

seconds 50

meters 400

second

meters

Please try this one in your notebook:

A cruise ship travels 3000 meters in 250 seconds. What is its speed?

My solution looks like this:

s =

s =

s = 12

t

d

seconds 250

meters 3000

second

meters

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

massV

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?

The solution looks like this:

d =

d =

d = 20

V

m

scentimeter cubic 25

grams 500

centimeter cubic

grams

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?

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

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.