# Velocity Acceleration Motion Notation – Physics

### Chapter 1 Velocity Acceleration Motion – Physics

In this chapter we discuss Velocity, Acceleration, Motion, and Notation – Physics.

Units

systems giving context to numbers

Length

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

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