Question

A body starts from rest with constant acceleration a, its velocity after n second is v. The displacement of body in last two seconds is ______.

Options

• `(2v(n - 1))/n`

• `(v(n - 1))/n`

• `(v(n + 1))/n`

• `(2v(n + 1))/n`

Answer 1

A body starts from rest with constant acceleration a, its velocity after n second is v. The displacement of body in last two seconds is `bbunderline((2v(n - 1))/n)`.

Explanation:

We know that, `s = ut + (a((t^2))/2)`

Here, object starts from u = 0 and time(t) = n

`s_n = 1/2an^2, s_{n - 2} = 1/2a(n - 2)^2`

Displacement in last 2 seconds,

`s = 1/2an^2 - 1/2a(n - 2)^2`

= `a/2(2n - 2)2` = 2a(n - 1)

But v = u + at

⇒ v = 0 + an or a = `v/n`

s = `(2v)/n(n - 1)`