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)`