Question

The speed of a body moving with uniform acceleration is $u$. This speed is doubled while covering a distance $S$. When it covers an additional distance $S$, its speed would become

• A. $\sqrt{5}u$
• B. $\sqrt{3}u$
• C. $\sqrt{11}u$
• D. $\sqrt{7}u$

Answer 1

The correct option is D $\sqrt{7}u$

Given speed of the body $=u$
From third equation of motion $v^2=u^2+2as...\left(i\right)$

When it covers distance 𝑆 its speed becomes double.
Therefore, from equation (𝑖)
$(2u{)}^2=u^2+2as$
$2as=3u^2$

Now, after covering an additional distance $s$, if velocity becomes $v$, then
$v^2=u^2+2a\left(2s\right)$
$v^2=u^2+4as$
$v^2=u^2+6u^2=7u^2$
$v=\sqrt{7}u$