The Big 5 KINEMATIC EQUATIONS

Formula 1:


This formula comes directly from the graph.
To find acceleration on a v -> t graph, you find the slope.

a = rise/run
a = ∆v / ∆t
a = (v2 - v1) / ∆t
a∆t = v2 - v1


Formula 2:


To find d on a v-> t graph, you find the area.

Area of a trapezoid: A = (a+b)h /2
d = (v1 + v2)∆t / 2
2d= (v1 + v2)∆t d = 1/2(v1 + v2)∆t


 Formula 3:


A and d must be included because they were already proven.

From Formula (1), isolate v2.v2 = a∆t + v1 =☺
Sub ☺ into Formula (2).
d = 1/2(v1 + ☺)∆t
d = 1/2(v1 + a∆t + v1)∆t
d = 1/2∆t(2v1 + 2∆t)d = v1∆t + 1/2a∆t²

Formula 4:


From Formula (1), isolate v1.v1 = a∆t - v2 =☻
d = 1/2(☻+ v2)∆t
d = 1/2(-a∆t + v2 + v2)∆t
d = 1/2∆t(-a∆t +2v2)
d = v2∆t - 1/2a∆t²

Formula 5:


Isolate ∆t from Formula 1.
a∆t = v2-v1
∆t = v2 - v1/a = A
sub A into Formula (2).
d = 1/2(v1 + v2)(v2 - v1/a)
ad = 1/2(v2 + v1)(v2 - v1)
2ad = v2² - v1²v2² = v1² + 2ad

There is another method of doing Formula 5, but I prefer this method.