Deriving Equation 3

- Deriving Equation 3: d=V1Δt + ½aΔt²
 Our goal in this equation is to find the displacement. We can do that by finding the area of the trapezoid made by the slope and the x axis. The equation basically divided the area of the trapezoid into two parts: a triangle and a rectangle.
The formula for the area of a triangle is A= bh/2. If we apply to that equation for the values on the triangle on the graph, the equation would be d= (v2-v1)Δt /2. To simplify this equation, we can replace (v2-v1) with aΔt. So the new equation would look like
d=½ (aΔt )Δt
d=½ aΔt²
and there we have the second part of equation 3 and now we have to derive the rectangular part.

The formula for the area of a rectangle is A=lw. If we apply to that equation for the values on the rectangle on the graph, the equation would be d= v1(t2-t1). We can simplify this equation further by replacing (t2-t1) with Δt.
 d=V1Δt and here we have the first part of equation 3.
Finally, we combine the two equations together and the result is d=V1Δt + ½aΔt² - equation 3. : )