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

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) √3u (B) √5u (C) √11u (D) √7u

Tardigrade Admin · Accepted Answer

As v2=u2+2as⇒ (2 u)2=u2+2as⇒ 2as=3u2 Now, after covering an additional distance s, if velocity becomes v, then, v2=u2+2a(2 s)=u2+4as=u2+6u2=7u2 ∴ v=√7u

Q. 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

$3 u$

$5 u$

$11 u$

$7 u$

As $v^{2} = u^{2} + 2 a s \Rightarrow (2 u)^{2} = u^{2} + 2 a s \Rightarrow 2 a s = 3 u^{2}$
Now, after covering an additional distance s, if velocity becomes v, then,
$v^{2} = u^{2} + 2 a (2 s) = u^{2} + 4 a s = u^{2} + 6 u^{2} = 7 u^{2}$
$∴ v = 7 u$

Q. 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

3​u

5​u

11​u

7​u