Motion

Uniformly accelerated motion with zero initial velocity

Equal-time displacement ratio 1:3:5:...

Equal-displacement time ratio 1:\(\sqrt{2}-1\):\(\sqrt{3}-\sqrt{2}\):...

If time ratio is \(\frac{1}{2}\):1:1:1:1... , displacement ratio is \(\frac{1}{8}\):1:2:3 or 1:8:16:24:...

Initial and final velocity being zero

\(\frac{t_1}{t_2}=\frac{x_1}{x_2}=\frac{a_2}{a_1}\)

If \(ma_1=(F-f)\) and \(ma_2=f\), \(\frac{F}{f}=\frac{t_1+t_2}{t_1}=\frac{x_1+x_2}{x_1}\)

Equal-time return

\(x_1:x_2=1:1\) \(v_1:v_2=1:2\) \(a_1:a_2=1:3\)