We can take Δ Δ r by adding the top area and the bottom area. The bottom area is a rectangle, and the area of a rectangle is the A ⋅ ⋅ B where A is the width and B is the height. In this case A = t and B = v 0 (the A here is different from the acceleration a ). This means that the bottom area is t v 0 . Now let's find the top area (a triangle). The area of a triangle is 1 2 B H where B is the base and H is the height. In this case, B = t and H = a t or A = 1 2 B H = 1 2 a t t = 1 2 a t 2 = a t 2 2 . Adding v 0 t and a t 2 2 results in the equation Δ Δ r results in the equation Δ Δ r = v 0 t + a t 2 2 . This equation is applicable when the final velocity v is unknown.