Algebra you need to know for physics:

Find x in terms of a, b and c for each problem. Letters represent numbers. (Note: if you can do these right away, you are ready for the typical physics course. If you cannot, find some math software or a math softperson for help.)

1. ax - b = c (get hint 1)

2. a/x = b/c hint 2

3. (a+b)/c = ax + 1/c hint 3

4. ax2 = b hint 4

5. ax2 + bx + c = 0 no hint. Memorize the solution near the bottom of the page.

PROPORTIONS: Sometimes doubling one quantity causes another one to double. This is the direct proportion if it holds in general (multiplying one by a number causes the other to be multiplied by the same number). Cases like this are related thusly: If y = cx, where c is a constant, then y is proportional to x.

Other times, things are inversely proportional: doubling one cuts the other in half. These have the form, y = c/x, or xy is constant. Then x and y are inversely proportional.

It is not unusual for y to be proportional to x2, so y = cx2 .

Or an inverse square: y proportional to 1/x2 or y = c/x2 .

In all of these cases, look at the equation relating the quantities, or think about it if you don't have an explicit equation. Examples below.

1. I bought 12.5 gallons of gasoline for $27.49. My friend got x gallons of the same gas for $10.50. Find x. hint 5

2. A car travels distance x (measured from the starting point) in time t. Under certain conditions for a limited time, x = ct2 , where c is a constant. If it traveled 30 ft in 5 seconds, how far did it go in 6 seconds (measured from the starting point). hint 6

3. Earth's gravitational field g is proportional to the inverse square of the distance to the center of Earth. At the surface g is 9.8 N/kg (which means that the chunk of matter we call a kilogram has a force of gravity acting on it equal to 9.8 Newtons). How far out in space (how many Earth radii) would you need to go to find g = 2 N/kg? hint 7

Answers to the five algebra problems:

1. x = (c+b)/a

2. x = ac/b

3. x = (a+ b-1)/ca

4. x = +- (b/a)1/2 (Note: to the 1/2 power means square root; and +- means + or -)

5. x = [-b +- (b2 - 4ac)1/2 ]/2a

Solutions to the proportion problems:

1. x/10.5 = 12.5/15, so x = (10.5)(12.5)/15 = 8.75 gallons (check the units: (gal)($)/($) = gal).

2. x/62 = 30/52, so x = (36)(30)/26 = 43.2 ft (check units: ft(s2 )/s2 = ft).

3. gR2 = constant, so if n is the number of radii you need, the distance is nR.
So 2(nR)2 = 9.8R2 , hence 2n2 =9.8 (since R2 cancels out), hence n = 4.91/2 (the square root of 4.9). n = 2.2, rounded off to two digit precision. Notice that the units all cancel, so n is a pure number.

Notice that units are treated algebraically. This is exploited in converting units.

Before taking my first calculus course, I learned from the wisdom on a lavatory wall that the integral of d(cabin)/cabin is natural log cabin. I had heard of natural logs before, so I figured that this was significant stuff. It is. This is just a way of saying the integral of dx/x is lnx. If you are taking a course in physics with calculus, you may want to click on my underground calculus.

Do not click on back or your brain will be overloaded with numbers and will crash.

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Questions, comments: fredrick.gram @tri-c.edu or look up stuff in my index.