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 $2 s$ is:

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

Answer 1

Answer: (A)

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