### 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