Question

A body initially at rest is moving with uniform acceleration $a$. Its velocity after $n$ second is $\upsilon$ . The displacement of the body in $2s$ is:

• A. $\frac{2v(n-1)}{u}$
• B. $\frac{\upsilon (n-1)}{n}$
• C. $\frac{V(n+1)}{n}$
• D. $\frac{2v(n+1)}{n}$

Answer 1

Answer: (A)

$u=0,a$ (uniform acceleration), $t=n$
$v$ (final velocity after $n$ seconds)
$v=0+an⟹v=$ an $⟶(1)$
$s_n$ (distance travelled in $n$ seconds) $=0+\frac{1}{2}a{n}^2$
$s_{n-2}=\frac{1}{2}a(n-2{)}^2$
Distance travelled in least 2 seconds $=s_n-s_n-2$
$=\frac{1}{2}a\left[n^2-(n-2{)}^2\right]=\frac{1}{2}a\left[n^2-n^2-4+4x\right]=2an-2a⟶(2)$
From equation 1 and 2
$x=2a(n-1)$
$x=\frac{2v}{u}(n-1)$