Question

A particle starts from rest with uniform acceleration and its velocity after $n$ seconds is $v$. The displacement of the body in last two seconds is

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

Answer 1

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

From Newton’s first equation of motion
$v=0+na$
$⟹a=\frac{v}{n}$
Displacement in last two seconds:
$s\left(n\right)-s(n-2)$
$=(0+\frac{1}{2}a{n}^2)-(0+\frac{1}{2}a{(n-2)}^2)$
$s\left(n\right)-s(n-2)=2a(n-1)=2v\frac{(n-1)}{n}$
Final answer-(c)