Second Equation of Uniformly Accelerated Motion

Second equation of motion is used to calculate the position of an object after time t when it is undergoing constant acceleration a.

Suppose that at t = 0, x₁ = x₀; v₁ = v₀ and at t = t, x₂ = x; v₂ = v.

The distance traveled = area under v – t graph = Area of trapezium OABC

= ½(CB + OA) × OC

x – x₀ = ½(v + v₀)t

Since v = v₀ + at,

x – x₀ = ½(v₀ + at + v₀)t

x – x₀ = v₀t + ½at²

x = x₀ + v₀t + ½at²