Question

Mark the following statement is true or false.
If a ball starts falling from the position of rest, then it travels a distance of 25 m during the third second of its fall.

Answer 1

Let $S\left(n\right)=$ distance travelled by ball in $n^{th}$ second.

$\Rightarrow$ $S\left(n\right)=S_n-S_{n-1}$

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

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

$S\left(n\right)=\frac{10}{2}(2n-1)=5(2n-1)$

$S\left(3\right)=5(6-1)=25m$

$\therefore$ Statement is true.