Question

A particle starts moving from rest with uniform acceleration. It travels a distance $x$ in first $2$ seconds and distance $y$ in the next $2$ seconds. Then:

• A. $y=3x$
• B. $y=4x$
• C. $y=x$
• D. $y=2x$

Answer 1

The correct option is A $y=3x$

Let the acceleration of the particle be $\alpha$.

Initial velocity $v_i=0$

$\therefore$ Distance travelled in $2$ seconds: $x=v_{i}t+\frac{1}{2}\alpha t^2$ where $t=2$ s

$\therefore$ $x=0+\frac{1}{2}\alpha (2{)}^2=2\alpha$ ..........(1)

Distance travelled in $4$ seconds: $S=v_{i}t+\frac{1}{2}\alpha t^2$ where $t=4$ s

$\therefore$ $S=0+\frac{1}{2}\alpha (4{)}^2=8\alpha$ ............(2)

$⟹$ Distance traveled in last $2$ seconds: $y=8\alpha -2\alpha =6\alpha$

$\therefore$ $\frac{y}{x}=\frac{6\alpha }{2\alpha }$ $⟹y=3x$