Question

A particle starts moving from rest with uniform acceleration. It travels a distance X in the first three seconds and a distance Y in next three seconds, then :

• A. Y = X
• B. Y = 3X
• C. Y = 2X
• D. Y = 4X

Answer 1

The correct option is B Y = 3X

Let the acceleration of the particle be $a$.

Initial speed of the particle $u=0m/s$

Distance travelled by it in first 3 seconds, $X=ut+\frac{1}{2}a{t}^2$ where $t=3$ s

$\therefore$ $X=0t+\frac{1}{2}a(3{)}^2$

We get $X=4.5a$ ....(1)

Velocity of the particle after $t=3$ s, $v=u+at$

$\therefore$ $v=0+a\left(3\right)=3a$

Distance covered by it next 3 seconds, $Y=vt+\frac{1}{2}a{t}^2$ where $t=3$ s

$\therefore$ $Y=\left(3a\right)3+\frac{1}{2}a(3{)}^2=13.5a$ .....(2)

From (1) and (2), we get $Y=3X$