Question

A particle starting with certain initial velocity and uniform acceleration covers a distance of $12m$ in first $3s$ and a distance of $30m$ in next $3s$. The initial velocity of the particle is

• A. $3m{s}^{-1}$
• B. $2.5m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $1.5m{s}^{-1}$
• E. $1m{s}^{-1}$

Answer 1

The correct option is E $1m{s}^{-1}$

Given,
$s_1=12m,t_1=3s$
$s_2=30+12=42m$
$t_2=3+3=6s$
$\because s=ut+\frac{1}{2}a{t}^2$
$\therefore s_1=u{t}_1+\frac{1}{2}a{t}_1^2$
$12=3\times u+\frac{1}{2}a\times 3^2$
$12=3u+\frac{9}{2}a$ ...(i)

Similarly, $42=6u+\frac{1}{2}a\left(36\right)$ ...(ii)

Solving the Eqs. (i) and (ii), we get
$a=2m/s^2$,
$u=1m/s$
u is initial velocity.