Question

The distances covered by a freely falling body in its first, second, third,..... $n^{th}$ seconds of its motion

• A. forms an arithmetic progression
• B. forms a geometric progression
• C. do not form any well defined series
• D. form a series corresponding to the difference of square root of the successive natural numbers

Answer 1

Answer: (A)

Distance travelled by a body in $n^{th}$ second is $D_n=u+\frac{a}{2}\left(2n-1\right)$
Here, $u=0$, $a=g$
$\therefore$ Distance travelled by the body in $1^{st}$ second is $D_1=0+\frac{g}{2}\left(2\times 1-1\right)=\frac{1}{2}g$
Distance travelled by the body in $2^{nd}$ second is $D_2=0+\frac{g}{2}\left(2\times 2-1\right)=\frac{3}{2}g$
Distance travelled by the body in $3^{rd}$ second is
$D_3=0+\frac{g}{2}\left(2\times 3-1\right)=\frac{5}{2}g$
and so on.
Hence, the distances covered by a freely falling body in its first, second, third.....$n^{th}$ second of its motion forms an arithmetic progression.