Question

A particle moving with a uniform acceleration travels $24m$ and $64m$ 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

Answer: (C)

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