Question

A body initially at rest is moving with uniform acceleration a. Its velocity after n seconds is v. The displacement of the body in last 2 s is :

• A. $\frac{2v(n-1)}{u}$
• B. $\frac{v(n-1)}{n}$
• C. $\frac{v(n+1)}{n}$
• D. $\frac{2v(n+1)}{n}$

Answer 1

The correct option is A $\frac{2v(n-1)}{u}$

$u=0,a\text{(uniform acceleration)},t=n$

$v$ (final velocity after $n$ seconds)

$v=0+an⟹v=an⟶\left(1\right)$

$s_n$ (distance travelled in $n$ seconds)$=0+\frac{1}{2}a{n}^2$

$s_{n-2}=\frac{1}{2}a(n-2{)}^2$

Distance travelled in least $2$ seconds $=s_n-s_n-2=\frac{1}{2}a[n^2-(n-2{)}^2]=\frac{1}{2}a[n^2-n^2-4+4x]=2an-2a⟶(2)$

From equation $1$ and $2,$

$x=2a(n-1)x=\frac{2v}{u}(n-1)$