Equations and Constants

This page contains equations and constants that you may find useful during this course. You are welcome to print a copy of this page and use it during tests but you may not annotate this page in any way if you are going to use it in a test situation - it is your responsibility to understand these equations and their limitations...

Equations

• v_av = (x₂ - x₁) / (t₂ - t₁) = Δx / Δt
• v = dx / dt
• v_av = (r₂ - r₁) / (t₂ - t₁) = Δr / Δt
• v = dr / dt
• a_av = (v₂ - v₁) / (t₂ - t₁) = Δv / Δt
• a = dv / dt

The next 5 equations assume that the acceleration is constant and that motion is linear:

• a = (v - v₀) / t
• v = v₀ + a t
• Δx = ½ (v + v₀) t
• Δx = v₀ t + ½ a t ²
• v² = v₀² + 2 a Δx

• F_cent = mv² / r
• F_net = ma
• W = mg
• f_s <= µ_s n
• f_{s max} = µ_s n
• f_k <= µ_k n
• µ = tan θ where θ is the angle of the inclined plane relative to the horizontal
• component of weight perpendicular to inclined plane = n = mg cos θ
• component of weight parallel to inclined plane = mg sin θ
• p = m v
• F t = Δp

Constants

g = 9.81 m / s² (you may take g = 10 m / s² unless told otherwise)

Density of water = 1000 kg / m³

Density of air at atmospheric pressure and 20°C = 1.2kg / m³