Equations used to find properties of objects that move with constant acceleration

s - displacement, u - initial velocity, v - final velocity, a - acceleration , t - time

1 - We know that on a velocity-time graph, the starting velocty is u and the final velocity is v, 2 - We know that the gradient of the time = the acceleration = change in y / change in x, 3 - Therefore a = (v - u) / t, 4 - Rearrange for v = u + at

1 - We know that on a velocity-time graph, the starting velocity is u and the final velocity is v, 2 - We know that the displacement is the area under a velocity-time graph, 3 - Assuming the graph takes the shape of a trapezium, the area is (a + b / 2) × h, 4 - Taking a as u, b as v, and h as t, substitute to find the equation s = t(u + v / 2)

1 - We know that t = (v - u)/a and s = t(u + v / 2), 2 - Eliminate t from the equation by substituting to get the equation s = (v - u /a)(u + v / 2), 3 - Rearrange to get 2as = v² - u², 4 - Rearrange for v²

1 - We know that v = u + at and s = t(u + v / 2), 2 - Eliminate v by substituting to get the equation s = t(u + u + at / 2), 3 - Therefore s = t(2u/2 + at/2), 4 - Therefore s = t(u + ½at), 5 - Therefore s = ut + ½at²

1 - We know that u = v - at and s = ut + ½at², 2 - Eliminate u by substituting to get the equation s = t(v - at) + ½at², 3 - Therefore s = vt - at² + ½at², 4 - Therefore s = vt - ½at²