Question

With usual notation, the following equation, said to give
the distance covered in the nth second. i.e.,
(2n - 1)
Si= ut a
is
2​

Answer 1

Answer:

Explanation:

The distance travelled in a time t is:

s=ut+12at2

So the distance travelled between t and t−Δt is:

Δs=s(t)−s(t−Δt)=ut+12at2−u(t−Δt)−12a(t−Δt)2=uΔt+12a(2tΔt−Δt2)

The equation you cite is obtained by setting Δt=1, but remember that you're setting Δt equal to one second not the dimensionless quantity 1. So your equation should really be:

Δs=u⋅(1 second)+12a(2t(1 second)−(1 second)2)

or multiplying this out:

Δs=u⋅(1 second)+at(1 second)−12a(1 second)2

So it is dimensionally consistent.

It is also numerically correct