Equation 4 Relation to the V/T Graph

Equation 4: d=V2Δt-½aΔt²

This is the second equation used to determine the displacement (d), and since we are required to first calculate the area between the slope and x-axis, there are two methods of doing this. The first method was equation 3, add the area of the small rectangle to the triangle. The second method is to calculate the area of the large rectangle and subtract the area of the triangle.

Coincidently, there are two parts. V2Δt and ½aΔt² where the first part is the rectangle and the second one is the triangle.

The area of a rectangle is Base x Height whereas V2 is the height and t2-t1 is the base.
A = v2(t2-t1)
A = v2(Δt)

The area of the triangle is Base x Height / 2 whereas v2-v1 is the height and t2-t1 is the base. But from equation 1: v2-v1=aΔt.
A = ½Δt(v2-v1)
A = ½ΔtaΔt
A = ½aΔt²

Thus, d=V2Δt-½aΔt²