Question

A particle starts moving from rest under uniform acceleration. It travels a distance $x$ in the first two seconds and a distance $y$ in the next two seconds. If $y=nx$, then $n$ is equal to_____

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

Distance travelled in first two seconds, $x$,
$x=u\left(2\right)+\frac{1}{2}a(2{)}^2=\frac{1}{2}(4a)$ (As the $u=0$)

Now, distance travelled in next two seconds, y = distance travelled in four seconds $-$ distance travelled in two seconds
$y=s_u-x=\left[u\right(4)+\frac{1}{2}a(4{)}^2]-[u\left(2\right)+\frac{1}{2}a\left(2{)}^2\right]$
$=\frac{1}{2}a[4^2-2^2]=\frac{a}{2}\times 12$

Finding ratio of $y$ and $x$,
$\frac{y}{x}=\frac{\frac{a}{2}\times 12}{\frac{a}{2}\times 4}=3$

$\Rightarrow y=3x,$ hence $n=3$