Math For Physical Science
- 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.
- 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.