Question

A body starting from rest moving with uniform acceleration has a displacement of $16m$ in first $4s$ and $9m$ in first $3s$. The acceleration of the body is

• A. $1m{s}^{-1}$
• B. $2m{s}^{-1}$
• C. $3m{s}^{-1}$
• D. $4m{s}^{-1}$

Answer 1

The correct option is B $2m{s}^{-1}$

Given,

$u=0m/s$

$s=16m,t_1=4s$

$s^{\prime }=9m,t_2=3s$

The displacement in $4^{th}$ sec,

$s_4=s-s^{\prime }$

$s_4=16-9=7m$

The distance covered in $n^{th}$ second,

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

$s_4=0+\frac{a}{2}(8-1)$

$7=\frac{7a}{2}$

$a=2m/s^2$

The correct option is B.