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 $2s$ is:

• A. $\frac{2v(n-1)}{n}$
• 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 $\frac{2v(n-1)}{n}$

Here, $a=\frac{v-u}{t}=\frac{v-0}{n}=\frac{v}{n}$

Displacement in last $2s$:
$S_n-S_{n-2}=\frac{1}{2}a{n}^2-\frac{1}{2}a(n-2{)}^2$

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

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