Question

For a body moving with uniform acceleration, the displacement of the body in successive seconds is in the ratio of 1: 3: 5: 7. (True/False)

Answer 1

Displacement for $n^{th}$ second can be given as

$S_n=u+\frac{a}{2}(2n-1)$

Here initial vel is zero

So,

$S_n=0+\frac{a}{2}(2n-1)$

$\Rightarrow \frac{a}{2}(2n-1)$

for successive time periods

i.e $n,n+1,(n+2)$

for $t=n$

$S_n=\frac{a}{2}(2n-1)$

$t=n+1$

$S_{n+1}=\frac{a}{2}\left(2\right(n+1)-1)$

$=\frac{a}{2}.[2n+1]$

$t=n+2$

$S_n+2=\frac{a}{2}\left[2\right(n+2)-1]$

$=\frac{a}{2}.[2n+3]$

$S_n:S_{n+1}:S_{n+2}\Rightarrow \frac{a}{2}(2n+1):\left(\frac{a}{2}\right(2n+3\left)\right)$

Put $n=1$

$S_n:S_{n+1}:S_{n+2}\frac{a}{2}.1:\frac{a}{2}.3:\frac{a}{2}.5...$

$=1:3:\mathrm{5...}$