Physics: Vectors, Scalars, and Kinematics

Vocabulary and key formulas from lecture notes on Vectors, Scalars, SI Units, and Kinematics (SUVAT).

Vector

A quantity that has both magnitude and direction; examples include Force, velocity, acceleration, and displacement.

Scalar

A quantity that has magnitude only; examples include mass, length, Speed, temperature, time, momentum, energy, and work done.

Resultant Force ($F_{R}$) Calculation for perpendicular vectors

Found using the Pythagorean theorem: $F_{R} = \sqrt{F_{x}^{2} + F_{y}^{2}}$.

Vertical component ($F_{y}$) of a vector

$$F_{y} = F \times \sin(\theta)$$

Horizontal component ($F_{x}$) of a vector

$$F_{x} = F \times \cos(\theta)$$

SI Base Unit: Length

$\text{m}$ (meter)

SI Base Unit: Mass

$\text{kg}$ (kilogram)

SI Base Unit: Time

$\text{s}$ (seconds)

SI Base Unit: Temperature

$\text{k}$ (kelvin)

SI Base Unit: Current

$\text{A}$ (ampere)

SI Base Unit: Amount of substance

$\text{mol}$ (number of moles)

SI Base Unit: Light intensity

$\text{cd}$ (candela)

Newton ($N$) in SI base units

$$N = \text{kg}\,\text{m}\,\text{s}^{-2}$$

Joule ($J$) in SI base units

$$J = \text{kg}\,\text{m}^{2}\,\text{s}^{-2}$$

Prefix: k (kilo)

$$10^{3}$$

Prefix: m (milli)

$$10^{-3}$$

Prefix: c (centi)

$$10^{-2}$$

Prefix: M (mega)

$$10^{6}$$

Prefix: $\mu$ (micro)

$$10^{-6}$$

Prefix: d (deci)

$$10^{-1}$$

Prefix: G (giga)

$$10^{9}$$

Prefix: n (nano)

$$10^{-9}$$

Prefix: T (term)

$$10^{12}$$

Prefix: p (pico/pica)

$$10^{-12}$$

Average Speed

$$\text{total distance} / \text{total time}$$

Average Velocity

$$\text{total displacement} / \text{total time}$$

Acceleration ($a$)

The rate of change of velocity, calculated as $a = \frac{\Delta v}{t} = \frac{v_{f} - v_{i}}{t}$.

Displacement-Time Graph: Slope

The slope represented as $\frac{\Delta s}{\Delta t}$ equals the velocity ($v$).

Velocity-Time Graph: Slope

The slope represented as $\frac{\Delta v}{\Delta t}$ equals the acceleration ($a$).

Velocity-Time Graph: Area under the graph

Represents the displacement traveled.

SUVAT Equation: $v$

$$v = u + at$$

SUVAT Equation: $s$ (with acceleration)

$$s = ut + \frac{1}{2}at^{2}$$

SUVAT Equation: $v^{2}$

$$v^{2} = u^{2} + 2as$$

SUVAT Equation: $s$ (with initial and final velocity)

$$s = \frac{1}{2}(u + v)t$$

Free Fall acceleration ($g$)

$9.81\,m/s^{2}$ (referenced as $10\,m/s^{2}$ for exams).