Work, Energy and Power — Formula Sheet

W = F·d·cosθ

W = F⃗ · d⃗ (dot product)

W = ΣF(x)·Δx (variable force)

W_gravity = mgh (downward motion) or W_gravity = -mgh (upward motion)

W_spring = ½kx²

P = W/t = ΔW/Δt

P_instantaneous = dW/dt = F·v·cosθ

1 hp = 746 W

KE = ½mv²

W_net = ΔKE = KE_f - KE_i = ½mv₂² - ½mv₁²

p = mv and KE = p²/2m

PE_gravity = mgh

PE_spring = ½kx²

F_spring = -kx (Hooke's Law)

Work = (Component of force along displacement) × (Displacement) = F cos θ × d

Average Power = Total Work Done / Total Time Taken.

Kinetic Energy (KE) is the energy possessed by an object due to its motion. KE = ½mv².

W = Fd cosθ — Work equals force times displacement times cosine of angle between them

Work done by external force on spring = (1/2)kx² — this is stored as elastic potential energy

Power = Work done / Time taken = W/t, and also P = F·v (force times velocity)

SI unit of power is Watt (W) = J/s; Dimensional formula is [ML²T⁻³]

1 kW = 10³ W; 1 MW = 10⁶ W; 1 hp = 746 W

Average Power

P = ΔW/Δt.