Number of liters in a gallon:
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.
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(m) + log(n)
log(m) - log(n)
Numbers with magnitude and direction (e.g. displacement, velocity, acceleration, and force)
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:
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.
A change in position in space. A vector quantity.
Displacement / Time
lim( t → 0) Displacement / Time
The rate of change in velocity over time. A vector quantity.
Acceleration results from:
an application of force
deltaV / deltaT
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:
Acceleration due to gravity:
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 accleration implies:
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.
Constant Acceleration Equation: Vf =
= Vi + at
Constant Acceleration Equation: Vf2 =
= Vi2 + 2a(ΔX)
Constant Acceleration Equation: ΔX =
= average velocity / time
= Vit + 1/2at2
Constant Acceleration Equation: Average Velocity =
= ΔV / 2