Question

A particle moving with a uniform acceleration travels $24\, m$ and $64\,m$ in the first two consecutive interval of $4s$ each. Its initial velocity will be

• A. 5 m/s
• B. 3 m/s
• C. 1 m/s
• D. 4 m/s

Answer 1

The Correct Option is C

From equation of motion, we have
$s=u t+\frac{1}{2} a t^{2}$
where $s$ is displacement, $u$ is initial velocity, a is acceleration and $c$ is time.
When $s=24 \,m, t=4 s$,
we have
$24=4 u+\frac{1}{2} a(4)^{2}$
$\Rightarrow 24=4 u+8 a$
$\Rightarrow 6=u+2 a \,\,\,...$(i)
When body travels a total distance of $24+64=88$ min $8 s$, we get
$88=8 u+\frac{1}{2} a(8)^{2}$
$\Rightarrow 88=8 u+32 a$
$\Rightarrow 11=u+4 a \,\,\,...$(ii)
Solving Eqs. (i) and (ii), we get
$u=1\, m / s$