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 geomatic 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

The correct option is A forms an arithmetic progression

$x_1=0+\frac{1}{2}\left(g\right)(1{)}^2=5m$

$x_1+x_2=0+\frac{1}{2}\left(g\right)(2{)}^2=20m⟹x_{2}15m$

$x_1+x_2+x_3=0+\frac{1}{2}\left(g\right)(3{)}^2=45m⟹x_3=25m$

$x_1+x_2+\dots \dots x_n=0+\frac{1}{2}\left(g\right)(n{)}^2=5n^{2}m⟹x_n=5n^2-[5(n-1{)}^2]=10n-5=5+10(n-1)$

$⟹x_1,x_2,\dots \dots x_n$ forming an $AP$ with $d=10.$