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)

Forms an arithmetic progression

Answer 2

Distance travelled by a body in nth second is $\mathrm { D } _ { \mathrm { n } } = \mathrm { u } + \frac { \mathrm { a } } { 2 } ( 2 \mathrm { n } - 1 )$

Here, u = 0, a = g

$\therefore$Distance travelled by the body in 1^st seconds is $D _ { 1 } = 0 + \frac { g } { 2 } ( 2 \times 1 - 1 ) = \frac { 1 } { 2 } g$

Distance travelled by the body in 2^nd seconds is

$D _ { 2 } = 0 + \frac { \mathrm { g } } { 2 } ( 2 \times 2 - 1 ) = \frac { 3 } { 2 } \mathrm {~g}$

Distances travelled by the body in 3^rd seconds is

$\mathrm { D } _ { 3 } = 0 + \frac { \mathrm { g } } { 2 } ( 2 \times 3 - 1 ) = \frac { 5 } { 2 } \mathrm {~g}$

and so on.

Hence, the distances covered by a freely fallings body in its first, second, third …..nth second of its motions forms an arithmetic progression.