How equation #3 translates into the v/t graph

                               
Equation #3  ────   d = V1Δt + 1/2 aΔt²
                                          ↓             ↓
                                   rectangle   triangle

As the graph above, we know that we have to calculate the area of the trapezoid to find out the displacement. But, in Equation #3, only V1 is usable. We would break down the trapezoid into a triangle and rectangle.

To determine the area of the rectangle, we would multiple V1 (as symbol "a" shown in the graph《Width》) to t2 - t1, which known as Δt. (as symbol "h" shown in the graph《Height》)

It will give us a equation of  Area of rectangle = V1Δt

To determine the area of the triangle, we would multiple (V2 - V1) 《Base》to  Δt 《Height》divided by 2

According to Equation #1 aΔt = V2 - V1, so, as we sub this equation,
Area of triangle = ½(V2 - V1)(Δt)
Area of triangle = ½aΔt(Δt)
                        
Displacement = Total Area

Displacement = Area of rectangle + Area of triangle  (As we sub the equations in,)

Displacement = ½V1Δt + aΔt²