Chapter 1 Velocity Acceleration Motion – Physics
In this chapter we discuss Velocity, Acceleration, Motion, and Notation – Physics.
Units
systems giving context to numbers
meter (m)
Mass
kilogram (kg)
Force
newton (N)
Time
second (s)
Work
joule (J)
Energy
joule (J)
Power
watt (W)
giga
(G or B), 10^9
mega
(M), 10^6
kilo
(k), 10^3
centi
(c), 10^-2
milli
(m), 10^-3
micro
(µ), 10^-6
nano
(n), 10^-9
pico
(p), 10^-12
Scientific Notation
a method of writing very large or very small numbers by using powers of ten;
0.0000000004 = 4x 10^-10 or
500,000,000,000,000 = 5 x 10^14
Significand
the number before the power of 10 in scientific notation, such as the number 5 in the scientific notation 5 x 10^14
Scientific Notation Multiplications
multiply the significands and then add the exponents;
(4 x 10^-10)(5 x 10^14) = 2 x 10^5
– multiplying 4 by 5 = 20 (converted to 2)
– adding -10 and 14 = 4
Scientific Notation Divisions
divide the significand in the numerator (top) by the significand in the denominator (bottom) and then subtract the exponent in the denominator from the exponent in the numerator;
(4 x 10^-10) / (5 x 10^14) = 8 x 10^-25
– dividing 4 by 5 = 0.8 (convert to 8)
– subtracting 14 from -10 = -24
Scientific Notation Raised to a Power
raise the significand to that power and then multiply the exponent by that number;
(6.0 x 10^4)^2 = 3.6 x 10^9
– squaring (^2) 6.0 = 36.0 (convert to 3.6)
– multiplying 4 by 2 (10^4 x 2) = 8
Scientific Notation Additions
exponents must always be the same (if not convert one), and then add the significands together;
3.7 x 10^4 + 1.5 x 10^3 = 3.9 x 10^4
– converting 1.5 x 10^3 = 0.15 x 10^4
– adding 3.7 and 0.15 = 3.85 (round to 3.9)
Scientific Notation Subtractions
exponents must always be the same (if not convert one), and then subtract the significands;
3.7 x 10^4 – 1.5 x 10^3 = 3.6 x 10^4
– converting 1.5 x 10^3 = 0.15 x 10^4
– subtracting 1.5 from 3.7 = 3.55 (round to 3.6)
sin θ
SOH
= opposite / hypotenuse
= y / h
cos θ
CAH
= adjacent / hypotenuse
= x / h
tan θ
TOA
= opposite / adjacent
= y / x
Trigonometric Functions
the ratio relationship between the sides of right triangles
Logarithm
the power to which a base such as 10 (log) or “e” (ln) must be raised to get the desired number;
– log 45 = X (10^x = 45), so X = 1.6532
– ln 45 = Y (e^y = 45), so Y = 3.8067
Natural Log (“e”)
“e” = ln = 2.71828
Vectors
numbers that have both magnitude and direction, such as displacement, velocity, acceleration, and force
Scalars
numbers that have magnitude only, such as disctance, speed, energy, pressure, and mass
Resultant (R)
the sum or difference of two or more vectors
Pythagorean Theorem
X² + Y² = V² or, V = √X² + Y²
V = any vector (use V as the hypotenuse)
X = x component of vector V
Y = y component of vector V
Kinematics
branch of Newtonian mechanics that deals with the description of objects in motion which allows us to describe an objects velocity, speed, acceleration, and position with respect to time
Displacement (x)
an object in motions overall change in its position in space
Velocity (ν)
a vector quantity whose magnitude is speed and whose direction is the direction of motion;
v = displacement (x) / time (t)
SI units = meters/second (m/s)
Average Velocity
average velocity (v, with a line over it) = Δx / Δt
Speed (s)
the rate of actual distance traveled in a given unit of time:
s = distance (d) / time (t)
Instantaneous Velocity
the average velocity as the change in time approaches zero;
v = limΔx / Δt
Acceleration (a)
a vector quantity of the rate of change of velocity over time;
a = Δv / Δt
Average Acceleration
average acceleration (a, with a line over it) = Δv / Δt
Instantaneous Acceleration
the average acceleration as the change in time approaches zero;
a = limΔv / Δt
Linear Motion
the objects velocity and acceleration are along the line of motion. The pathway of the moving object is literally a straight line (one-dimensional motion), but not limited to vertical or horizontal paths
Acceleration due to Gravity (g)
g = 9.8 m/s²
Constant Acceleration
an object in motion who’s velocity is changing due to a constant force being applied
Kinematics Equations
the five equations applied to objects in motion with constant acceleration;
v = v0 + at
x – x0 = v0t + (at² / 2)
v² = v0² + 2a(x – x0)
average v = (v0 + v) / 2
Δx = (average v)(t) = [(v0 + v) / 2] t
Projectile Motion
an object in motion that follows a path along two dimensions and the velocity and acceleration are in two directions (usually horizontal and vertical) and separate from each other
Free Fall
objects in linear motion experiencing acceleration equal to that of gravity, discounting air resistance
Terminal Velocity
the constant velocity of a falling object when the force (net force = 0) of air resistance is equal in magnitude and opposite in direction to the force of gravity