Question

A particle starts from rest with uniform acceleration $a$. Its velocity after $n$ second is $v$. The displacement of the body in the last two second is

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

Answer 1

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

We know,
At $t=n$sec
$s_n=\frac{1}{2}a{n}^2$
$v^2=2a{s}_n$
$=2a\cdot \frac{1}{2}a{n}^2$
$=a^2{n}^2$
$\therefore v=an$
$\therefore a=\frac{v}{n}$ ...(i)
Now, $s_n-s_{n-2}=\frac{1}{2}a[n^2-(n-2{)}^2]$
$=\frac{1}{2}a[4n-4]$
$=2a(n-1)$ from (i)
$s_n-s_{(n-2)}=\frac{2v(n-1)}{n}$