Question

Prove that the distances traversed during equal intervals of time by a body falling from rest, stand to one another in the same fatio as the odd mumbers beginning with unity [namely 1: 3: 5: …………….].

Answer 1

Here, `u=0, a=g,
Distance travelled I nth second is given by
`D_(n) =u +a/2 (2n -1)`
Distance travelled in 1st` second`
[i.e. when `n=1] will be
Distance travelled in 2th second
[i.e. when `n=2 ] will be
`D_(2) 0+ g/2 92 xx1) =(3g)/2`
Distance travelled in 3th second
[i.e. when `n3 ] will be
`D_(3) 0+ g/2 (2 xx5-1) =(5g)/2`
Distance travelled in 4th second
[i.e. when 4n ] will be
`D_(4) =0+ g/2 (2 xx 4-4 -1) =(7g)/2`
`:. D_(1) : D_(2) : D_(3): D_(4) 1: 3: 5: 7 (Proved)`.