Motion in a Straight Line — Formula Sheet

Average Velocity (v̄) = Δx / Δt = (x₂ - x₁) / (t₂ - t₁)

Average Speed = Total Distance Travelled / Total Time Taken

Relative Velocity of B w.r.t. A: v_BA = v_B - v_A

Average Acceleration (ā) = Δv / Δt = (v₂ - v₁) / (t₂ - t₁)

Instantaneous Velocity: v = lim(Δt→0) (Δx/Δt) = dx/dt

Instantaneous Acceleration: a = lim(Δt→0) (Δv/Δt) = dv/dt

Average Velocity = Slope of x-t graph = Δx/Δt = BC/AC = tan θ

Acceleration = Slope of v-t graph = Δv/Δt = MP/LP = tan θ

Distance = Area under v-t graph

Area of trapezium = (1/2)(v₁ + v₂)(t₂ - t₁)

For a body at rest

the graph is a horizontal straight line parallel to the time axis (slope = 0, velocity = 0).

Standard notation

v₀ = initial velocity (at t=0), v = final velocity (at time t), a = constant acceleration, x₀ = initial position, x = final position, s = (x − x₀) = displacement.

First equation

v = v₀ + at — relates velocity to time. Derived from definition of acceleration.

Speed = total distance / total time; Velocity = displacement / time.

Average velocity = Δx / Δt; can be zero even if the body is moving.

Acceleration = rate of change of velocity = Δv/Δt.