Number of liters in a gallon:

3.785

How to multiply numbers in scientific notation:

multiply significands, add the exponents

How to divide numbers in scientific notation:

divide significands, subtract the exponents

A number raised to a power in scientific notation:

raise the significand by the number, multiply the exponents by that number

How to add/subtract numbers in scientific notation:

The numbers have to have the same exponents. If they do not, convert one of them so that they have the same exponents.

Logarithm

the log of a number for a given base is the power to which the base must be raised to equal that number. In other words, a base raised by some power will equal a number, and that power is the log of that base.

The two most common bases:

e (natural log; 2.71) and 10 (common log)

log(mn)=

log(m) + log(n)

log(m/n)=

log(m) - log(n)

log(m^{n})=

nlogm

Vectors are:

Numbers with magnitude and direction (e.g. displacement, velocity, acceleration, and force)

Scalars are:

Number with magnitude only and NO direction (e.g. distance, speed, energy, pressure, and mass)

The sume or difference of two vectors is called the:

resultant of the vectors

Whe adding vectors, add them:

tip-to-tail

A single vector can be broken up into:

X and Y components

Subtracting two vectors can be accomplished by:

Adding the opposite of the vector being subtracted. A - B = A + (-B). By "-B" we mean a vector with the same magnitude, just pointing in the opposite direction.

Displacement

A change in position in space. A vector quantity.

Velocity

Displacement / Time

Instantaneous Velocity

lim( t → 0) Displacement / Time

Acceleration

The rate of change in velocity over time. A vector quantity.

Acceleration results from:

an application of force

Average acceleration=

deltaV / deltaT

Instantaneous Acceleration

Defined as the average acceleration as time approaches zero.

lim ( t→0) ΔV / ΔT

On a velocity versus time graph, the tangent to the graph at any time (the slope) is the:

Instantaneous acceleration. (+ slope is + acceleration)

Falling objects exhibit linear motion with:

Constant acceleration

Acceleration due to gravity:

9.8 m/s^{2}

Projectile Motion

Motion that follows a path in two dimensions (horizontal and vertical). Each dimension must be analyzed separately.

In projectile motion, horizontal velocity is always:

constant

Constant accleration implies:

constant force

Objects in terminal velocity experience a net force of:

Zero. Therefore the acceleration is also zero. The upward force of the air resistance is equal and opposite to the downward force of gravity.

sin 0

0

cos 0

1

sin 30

0.5

cos 30

0.86

sin 45

0.71

cos 45

0.71

sin 60

0.86

cos 60

0.5

sin 90

1

cos 90

0

sin 180

0

cos 180

-1

Constant Acceleration Equation: V_{f} =

= V_{i} + at

Constant Acceleration Equation: V_{f}^{2} =

= V_{i}^{2} + 2a(ΔX)

Constant Acceleration Equation: ΔX =

= average velocity / time

= V_{i}t + 1/2at^{2}

Constant Acceleration Equation: Average Velocity =

= ΔV / 2