Question

A body starts from rest with uniform acceleration. If its velocity after $n$ seconds is $v$ then assuming straight line motion, its displacement in the last two seconds is:

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

Answer 1

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

$u=0$

$s=\frac{1}{2}a{t}^2$

Displacement at last $2s$

$=s_n-s_{n-2}$

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

$=a(2n-2)$

Now, $v=at⟹a=\frac{a}{n}$

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