Chapter 1: Units and Kinematics Flashcards
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(mn)=
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/s2
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: 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
