APPENDIX TO LESSON 1

Appendix to Lesson 1
Chapter 1 #9
a = 2xtp = (2)(m)(s-2), s-2 = 1/s2
Because
a. x is in units of meters (m)
b. t is in units of seconds (s)
c. p is the exponent (a number), and has to be “-2”,
Why? Because (s-2) ≡ 1/s2 (in this case, the symbol “≡” means “defined as” or “is the same as”

Remember, the units of acceleration, or, ‘a’ are m/s2

Remember, that distance, ‘x’ is in units of meters (m)

Also, velocity (speed), ‘v’ is distance/time, or, x/t, and it is in units of meters per second, ‘m/s’

acceleration ‘a’ is velocity/time = v/t = (m/s)/s = [m/(s)(s)] = m/s2.

s ≡ second
1/s ≡ per second (same as s-1)
1/s2 ≡ per second squared (same as s-2)
Meters times per second squared = (x)(s-2)

Other examples:
v = 3xtr, so what is “r” = -1
distance = 4xtw, so what is w? 0

Chapter 1 #19
1.0 m = 39.37 inches = 3 feet, 3.37 inches; 3.28 feet

23 m/s = 75 ft/sec = 0.0142 mi/sec = (0.0142 mi/s)(3600 sec/hour) = 51.13 mi/hr = 5.1 x 101 mi/hr

75 feet = 75/5280 = 0.0142 mi

Chapter 1 #31
(1 foot)3 = (30.48 cm)3 = 28,317 cm3. = 28,317 ml = 28.3 L, how many 0.42 L’s (mutchkin) fit into 28.3 L?
(28.3 / 0.42) = 67

1.0 gallon = 3.79 liters

1 noggin = 0.28(0.42 L) = 0.1176 L

So, how many (0.1176’s) go into 3.79?

3.79/0.1176 = 32
32 noggins = 1 gallon

Chapter 2 #9
200 meters = 0.2 km = (0.2 km)(5/8 mi/km) = 1/8 mi = 0.125 mi

0.125 mi/19.75 sec = 0.006329 mi/sec = (0.006329 mi/sec)(3,600 sec/hour) = 22.78 mi/hour

Chapter 2, #19

The relative speed of Jack to Jill is: v = 2.6 m/s; The distance traveled is10 meters; so, how long does it take to travel 10 meters at a speed of 2.6 m/s? Like this >>> (10m)/(2.6m/s) = 3.85 s (until Jack and Jill crash)

Since velocity is v = x/t, we know that the dog’s distance traveled is: x = v t = (3 m/s)(3.85 s) = 11.55 m.

Chapter 2, #25
y = ax2 + bx + c standard quadratic equation, but for this:

y = x
a = -2
b = 6
c = 0
x = t

x = -2t2 + 6t, as if it were y = -2x2 + 6x
make table, choose any number for x, then


x(t) y(x)
0s 0
1s 4
0.5s 2.5
etc.
After this, plot these dots, connect the dots…
… and “plug n chug” to get what x is for each “t” that is selected… 0 s, 1 s, etc.