Question

A body covers $40m$ in first $5sec$ and then covers $65m$ in next $5sec$ . Find the initial velocity of the body if it is moving with uniform acceleration.

• A. $4m{s}^{-1}$
• B. $2.5m{s}^{-1}$
• C. $5.5m{s}^{-1}$
• D. $11m{s}^{-1}$

Answer 1

Answer: (C)

We know, $S_1=ut+\frac{1}{2}a{t}^2$ ... $(i)$
$t_1=t_2=t$ (given)
and $v=u+at$
Now $S_2=vt+\frac{1}{2}a{t}^2$
putting value of $v$ in above equation $S_2=\left(u+at\right)t+\frac{1}{2}a{t}^2=ut+a{t}^2+\frac{1}{2}a{t}^2$ ... $(ii)$
Equation $\left(ii\right)-\left(i\right)=S_2-S_1=a{t}^2$
$\Rightarrow a=\frac{S_2-S_1}{t^2}=\frac{65-40}{{\left(5\right)}^2}=1m/s^2$
From equation $(i)$ , we get.
$S_1=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 40=5u+\frac{1}{2}\times 1\times 25$
$\Rightarrow 5u=27.5$
$\therefore u=5.5m/s$