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 last two seconds is

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

Answer 1

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

Initial velocity of body $u=0$

Let the acceleration be $a$.

Using $v=u+at$

We get $v=0+an$

$⟹a=\frac{v}{n}$

For displacement in last two seconds, $t=2$

Using $S=vt-\frac{a{t}^2}{2}$

Or $S=v\left(2\right)-\frac{v}{2n}(2{)}^2=\frac{2v(n-1)}{n}$

Correct answer is option B.