# Is the equation for displacement in the n th second dimensionally correct?

Is the equation for displacement in the n th second dimensionally correct?

S = u + a (n- 1/2)

Yes

See the explanation given by Vimal Raj

If we notice the derivation of this formula
let t1=x and t2=y (for my easiness)
S(y)=uy + 1/2 ay^2———-(1)
S(x)=ux + 1/2 ax^2———–(2)
sub (2) from (1)
S(y)-S(x)=uy + 1/2 ay^2 – ux – 1/2 ax^2
S(y)-S(x)=u(y-x)+a/2(y^2-x​^2)
here we know y-x =1 s ,then
Sn = u (1s) + a/2(y+x)(y-x)
Sn =u(1s) + a/2(y+x)(1s)

Dimension of Sn must be equal to u(1s)

u=LT^1
THEN Sn=[LT^1][T]=[L]