User:Darth Skynyrd/SF Formulae

Acceleration due to gravity

 * $$S = {\textstyle 1 \over 2} at^2.$$


 * S = Height above the ground (5 meters)
 * a = acceleration due to gravity
 * t = amount of time it took to fall (one second)


 * $$5 = {\textstyle 1 \over 2} 1^2a$$


 * $$5 = {\textstyle 1 \over 2} a$$


 * $$10 = {\textstyle a}$$

Thus the acceleration due to gravity must be 10 meters per second per second at the site.

Kinetic Energy

 * $$EK = {\textstyle 1 \over 2} mv^2$$


 * EK = Kinetic Energy
 * m = mass (e.g. 200 grams)
 * v = velocity (using new velocity of 10 m/s)


 * $$EK = {\textstyle 1 \over 2} (0.2)10^2$$


 * $$EK = {\textstyle 1 \over 2} (0.2) 100$$


 * $$EK = {\textstyle (0.1) 100}$$


 * $$EK = {\textstyle 10}$$

Thus the kinetic energy is 10 joules.

Potential Energy

 * $$EP = {\textstyle mgh}$$


 * EP = Potential Energy
 * m = mass (200 grams again)
 * g = acceleration due to gravity (we'll be using 10 m/s/s this time)
 * h = height above the ground (5 m)


 * $$EP = {\textstyle 0.2 (10) (5)}$$


 * $$EP = {\textstyle 2 (5)}$$


 * $$EP = {\textstyle 10}$$

Thus the potential energy is 10 joules, making it equal to the kinetic energy.

PU-0

 * 4 = speed she can ride Joan bike in minutes per mile
 * 6 = minutes it takes her to get her bicycle out, get ready to ride, and put her bike away
 * m = the number of minutes she rides
 * 4m+6 = total number of minutes her bike ride lasts

B
She rode 11 miles.


 * $$ {\textstyle 4m + 6}$$


 * $$ {\textstyle 4(11) + 6}$$


 * $$ {\textstyle 44 + 6}$$


 * $$ {\textstyle 50}$$

C
Her ride took 1 hour, 42 minutes.


 * $$ {\textstyle 4m + 6 = 102}$$


 * $$ {\textstyle 4m = 96}$$


 * $$ {\textstyle m = 24}$$

D
How many miles per hour was she pedalling in C?

4 minutes per mile = 60 minutes per x miles, or:


 * $$ {\textstyle 4 \over 1} = {\textstyle 60 \over x}$$


 * $$ {\textstyle 4x = 60}$$


 * $$ {\textstyle x = 15}$$

A

 * $$ {\textstyle x-4}$$

B

 * $$ {\textstyle 30x}$$


 * $$ {\textstyle 20(x-4)}$$

C

 * $$ {\textstyle 470 = 30x + 20(x-4)}$$


 * $$ {\textstyle 470 = 30x + 20x - 80}$$


 * $$ {\textstyle 550 = 50x}$$


 * $$ {\textstyle 11 = x}$$

D

 * $$ {\textstyle 30(11) = 330}$$


 * $$ {\textstyle 20(11-4) = 140}$$