Question

Distances covered by a freely falling body (starting from rest) during $1^{st},2^{nd},3^{rd}....n^{th}$ second of its motion are proportional to :

• A. even numbers
• B. odd numbers
• C. all integral numbers
• D. square of integral numbers

Answer 1

The correct option is B odd numbers

Distance travelled by a body in $n^{th}$ second (falling freely) is:
$S_n=\frac{1}{2}a{n}^2-\frac{1}{2}a(n-1{)}^2=\frac{1}{2}a(n^2-(n^2-2n+1))$

$=\frac{1}{2}a\underset{–}{(2n-1)}$
$\Downarrow$
(odd nos)

Since for $n$ integer $(2n-1)$ will always yield odd number, hence, correct answer is option B.