CAPE Physics Formulas Semester 1

Average speed

$$s=\frac{\Delta d}{\Delta t}$$

Average velocity

V= $\frac{\Delta d}{\Delta t}$

Average acceleration (a)

a = $\frac{v-u}{t}$

Kinematics Velocity

v = u + at.

Kinematics Velocity²

v² = u² + 2as.

Kinematics Displacement

$s=ut+\frac12at^2$

Momentum (p)

p = mv.

Rate of change of momentum

p=$\frac{m\left(v-u\right)}{t}$

Newton’s Second Law of Motion

F = ma.

Impulse

F = m(Δv/Δt)

Law of Conservation of Momentum (Elastic Collision)

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

Law of Conservation of Momentum (Inelastic Collision)

m₁u₁ + m₂u₂ = (m₁ + m₂)Vₗ.

Total Resultant Velocity (v)

v = √(vₓ² + vᵧ²).

Direction of Motion (θ)

θ = tan⁻¹(vᵧ/vₓ).

Time of Flight (T)

T = (2u*sin(θ))/g.

Maximum Height (H)

H = u²sin²(θ)/(2g).

Range (R)

R = (u²sin2θ)/g.

Angular Displacement (θ)

θ = s/r.

Angular Velocity (ω)

ω = θ/t or ω = v/r.

Period (T)

T = 2π/ω.

Frequency (f)

f = 1/T or f = ω/2π.

Linear Velocity (v)

v = ωr.

Centripetal Acceleration (aₜ)

aᶜ = v²/r or aᶜ = ω²r.

Centripetal Force (Fₜ)

Fₜ = mv²/r or Fₜ = mω²r.

Moment (T)

T = Fxd.

Work (W)

W = Fxx.

Kinetic Energy (Kₑ)

Kₑ = 1/2mv².

Gravitational Potential Energy (Eₚ)

Eₚ = mgh.

Power (P)

P = W/t.

Internal Energy (U)

U = Eₖ + Eₚ.

Specific Heat Capacity (Eₕ)

Eₕ = mcΔT.

Stefan's Equation (P)

P = σeA(T⁴ - Tₛ⁴).

Fourier’s Law

$$Q=kA\left(\frac{T<em>{h}-T</em>{c}}{L}\right)$$

Density

$$\rho=\frac{m}{v}$$

Pressure

$$P=\rho gh$$

Velocity after time formula

$$v<em>{y}=u</em>{y}-gt$$

Height after time formula

$$y=u_{y}t- rac12gt^2$$

Velocity after given height formula

$$v<em>{y}^2=u</em>{y}^2-2gy$$

Horizontal distance or range formula

$$x=u_{x}t$$