推导公式△s=aT^2

推导公式△s=aT^2
推导公式△s=aT^2

推导公式△s=aT^2
S=平均速度*t
S1=T*aT/2=(aT^2)/2
S2=2T*a*2T/2-T*aT/2=3(aT^2)/2
S3=3T*a*3T/2-2T*a*2T/2=5(aT^2)/2
S4=4T*a*4T/2-3T*a*3T/2=7(aT^2)/2
.
3(aT^2)/2-(aT^2)/2=5(aT^2)/2-3(aT^2)/2=7(aT^2)/2-5(aT^2)/2=aT^2
所以△S=aT^2

X1=VoT+aT^2/2

X2=Vo(2T)+a(2T)^2/2

X3=Vo(3T)+a(3T)^3/2

ΔX=(X3-X2)-(X2-X1)

将上面的各量代入

ΔX=aT^2