How to derive Equation #4 from a velocity graph

As we did with Equation #3 , it is possible to derive Equation # 4 from a velocity graph. It will be slightly different.

Equation #4 states: d = v2Δt - ½aΔt²

In order to get to our equation we need to follow several steps. First of all we need to find the area of the rectangle OCBD. We can find it using the formula for the area of a triangle which is: (A = lw).While on the graph it will be like this: (d = v2Δt) because we have to multiply v2 with (t2-t1)=Δt

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Secondly we need to find the area of the ACB triangle. The area of a triangle is [A = bh/2]. On our graph is will be rearranged as followed: ½aΔt² since aΔt is isolated from Equation 1, when we multiply  ½Δt with (aΔt) we will get ½aΔt².

 

Lastly in order to get the forth equation we need to subtract the area of the triangle ½aΔt² from the area of the big rectangle v2Δt. 

Our equation will end up looking like this:

d = v2Δt - ½aΔt²