Distance: How far something travels (scalar)

Displacement: Final difference in position (vector)

Average Velocity = total distance traveled / total time

$\text{Average velocity} = \frac{\Delta x}{\Delta t}$

Rate of change of velocity

$a = \frac{\Delta v}{\Delta t}$

$v = u + at$

Final velocity = Initial velocity + acceleration × time

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

Final position = Initial velocity × time + ½ × acceleration × time²

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

Final Velocity² = Initial Velocity² + 2 × Acceleration × Final Position

$s = \frac{v + u}{2} \cdot t$

Final position = average of initial and final velocity × time (only if acceleration is constant)

$g=9.8ms^{-2}$

Newton's First Law (Law of Inertia)

An object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by a net external force.

This means: Objects resist changes to their state of motion.

Newton's Second Law

The net force acting on an object is equal to the rate of change of its momentum. For constant mass:

$F = ma$

Where:
F = Net force (N)
m = Mass (kg)
a = Acceleration (m/s²)

Newton's Third Law

For every action, there is an equal and opposite reaction.

This means: Forces always come in pairs. If object A exerts a force on object B, then B exerts an equal and opposite force on A.

1. Static Friction

$f_{\text{static}} \leq \mu_s N$

Static friction resists the start of motion. It increases with applied force up to a maximum limit.

$f_{\text{static}}$ = Static friction force (N)

$\mu_s$ = Coefficient of static friction (unitless)

$N$ = Normal force (N)

2. Kinetic (Dynamic) Friction

$f_{\text{kinetic}} = \mu_k N$

Kinetic friction acts on objects in motion and stays constant.

$f_{\text{kinetic}}$ = Kinetic friction force (N)

$\mu_k$ = Coefficient of kinetic friction (unitless)

$N$ = Normal force (N)

Fluids

Work

$\text{Work} = \text{Force} \cdot \text{Distance} \cdot \cos(\theta)$

W = Work (Joules, J)

F = Force (Newtons, N)

d = Displacement (meters, m)

θ = Angle between force and displacement

Kinetic Energy

$E_k = \frac{1}{2} m v^2$

Ek = Kinetic Energy (J)

m = Mass (kg)

v = Velocity (m/s)

Gravitational Potential Energy

$E_p = m g h$

Ep = Gravitational Potential Energy (J)

m = Mass (kg)

g = Acceleration due to gravity (9.81 m/s²)

h = Height above reference point (m)

Elastic Potential Energy

$E_e = \frac{1}{2} k x^2$

Eₑ = Elastic Potential Energy (J)

k = Spring constant (N/m)

x = Displacement from equilibrium (m)

Power

$P = \frac{W}{t}$

P = Power (Watts, W)

W = Work done (J)

t = Time taken (s)

Efficiency

$\text{Efficiency} = \frac{\text{Useful Output Energy}}{\text{Total Input Energy}} \cdot 100\%$

Efficiency = Percentage of input energy converted into useful output

$\rho = mv$

$\rho$ = momentum

m = Mass

v = Velocity

Collisions

Momentum before collision = momentum collision no matter what

In 2 dimensions, the momentum is conserved in both axis individually