## Particle Under Constant Acceleration

The acceleration keep same throughout the motion. The velocity changes at the same rate throughout the motion. a = (v_f - v_i)/(t-0) => color(red)(v_(f) = v_(i) + at color(red)(v_(avg) = 1/2(v_i + v_f) The position changes at the same rate throughout the motion. x_f - x_i = color(blue)(v_(avg)) t => x_f - x_i = 1/2(v_i + v_f) times t => x_f = x_i + 1/2(v_i + color(blue)(v_f)) t => x_f = x_i + 1/2(v_i +color(blue)(v_(i) + at)) t => color(red)(x_f =x_i + v_i t +1/2at^2 )
v_f = v_i + at v_(avg) = (v_i + v_f)/2 x_f = x_i + 1/2(v_i + v_f)t x_f = x_i + v_it + 1/2 a t^2 v_f^2 = v_i^2 + 2a(x_f - x_i)