# 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

• vav = (x2 - x1) / (t2 - t1) = Δx / Δt
• v = dx / dt
• vav = (r2 - r1) / (t2 - t1) = Δr / Δt
• v = dr / dt
• aav = (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

• Fcent = mv² / r
• Fnet = ma
• W = mg
• fs <= µs n
• fs max = µs n
• fk <= µk 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