Question

The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is $8m/s^2$. The time taken by the particle to move the second metre is

• A. $\frac{\sqrt{2}-1}{2}s$
• B. $\frac{\sqrt{2}+1}{2}s$
• C. $(1+\sqrt{2})s$
• D. $(\sqrt{2}-1)s$

Answer 1

The correct option is A $\frac{\sqrt{2}-1}{2}s$

Given, acceleration $=8m/s^2$

We know $s_1=u{t}_1+\frac{1}{2}a{t}_1^2$

Therefore, $1=0+\frac{1}{2}\times 8\times t_1^2$

$\Rightarrow$ $t_1^2=\frac{1}{4}$

$\Rightarrow$ $t_1=\frac{1}{2}$

and $s_2=u{t}_2+\frac{1}{2}a{t}_2^2$

$\therefore$ $2=0+\frac{1}{2}8\times t_2^2$

$\Rightarrow$ $t_2^2=\frac{1}{2}$ $\Rightarrow$ $t_2=\frac{1}{\sqrt{2}}$

$\therefore$ Required time $=t_2-t_1$

$=\frac{1}{\sqrt{2}}-\frac{1}{2}=\frac{\sqrt{2}-1}{2}$s