Question

A particle moving with a uniform acceleration travels $24$ metre and $64$ metre in first two successive intervals of $4$ second each. Its initial velocity is

• A. $1m/s$
• B. $2m/s$
• C. $5m/s$
• D. $10m/s$

Answer 1

The correct option is A $1m/s$

$\left(\frac{v_1+u}{2}\right)t=24$

$\Rightarrow v_1+u=\frac{24\times 2}{4}=12$

$\Rightarrow v_1+u=12$----------------$\left(1\right)$

$\left(\frac{v_2+v_1}{2}\right)4=64$

$\Rightarrow v_1+v_2=32$---------------$\left(2\right)$

and $\left(\frac{v_2+4}{2}\right)8=88$

$\Rightarrow v_2+u=22$----------------$\left(3\right)$

from $\left(1\right)$ $\&$ $\left(2\right)$

$12-u+v_2=32$

$v_2-u=20$

from $\left(3\right)$ $\&$ $($)$

$\Rightarrow 24=2$

$\Rightarrow u=1m/s$

Hence,

option $\left(A\right)$ is correct answer.