Physics - Kinematics Question with Solution | TestHub

Solution:

Given: initial velocity $u=0$, constant acceleration $a$.

Velocity after $n$ seconds is $v$. So, $v=u+at⟹v=0+an⟹a=v/n$.

Displacement in $n$ seconds: $S_n=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}a{n}^2=\frac{1}{2}\left(\frac{v}{n}\right)n^2=\frac{1}{2}vn$.

Displacement in $(n-2)$ seconds: $S_{n-2}=\frac{1}{2}a(n-2{)}^2=\frac{1}{2}\left(\frac{v}{n}\right)(n-2{)}^2$.

Displacement in the last two seconds is $S_{last2}=S_n-S_{n-2}$.

$$S_{last2}=\frac{1}{2}vn-\frac{1}{2}\frac{v}{n}(n-2{)}^2$$

$$S_{last2}=\frac{v}{2n}[n^2-(n-2{)}^2]$$

$$S_{last2}=\frac{v}{2n}[n^2-(n^2-4n+4)]$$

$$S_{last2}=\frac{v}{2n}[4n-4]$$

$$S_{last2}=\frac{v}{2n}[4(n-1)]$$

$$S_{last2}=\frac{2v(n-1)}{n}$$

The final answer is $\boxed{\frac{2v(n-1)}{n}}$.