如何得出X=AT^2的?

s1=v0t+1/2at^2 ①

s2=v1t+1/2at^2 ②

......

sn=v(n-1)t+1/2at^2

v1=v0+at ③

将③代入②有:
s2=(v0+at)t+1/2at^2=v0t+at^2+1/2at^2
s2-s1=at^2

同理
sn-s(n-1)=at^2

xn=1/2*a*n^2*T^2-1/2*a*(n-1)^2*T^2
xn=1/2*a*T^2*(2n-1)
△x=X(n+1)-Xn =1/2*a*T^2*(2n+1)-1/2*a*T^2*(2n-1)
△x=a*T2