Question

A body is moving with uniform acceleration describes$40m$in the first$5sec$ and $65m$ in next $5sec$. Its initial velocity will be

• A. 4 m/s
• B. 2.5 m/s
• C. 5.5 m/s
• D. 11 m/s

Answer 1

The correct option is C 5.5 m/s

$\because S_1=ut+\frac{1}{2}a{t}^2.........\left(i\right)$

and velocity after first t sec
$v=u+at$

Now, $S_2=vt+\frac{1}{2}a{t}^2$

$=(u+at)t+\frac{1}{2}a{t}^2............\left(ii\right)$
Equation (ii)-(i) $\Rightarrow S_2-S_1=a{t}^2$

$\Rightarrow a=\frac{S_2-S_1}{t^2}=\frac{65-40}{(5{)}^2}=1m/s^2$

From equation (i), we get,
$S_1=ut+\frac{1}{2}a{t}^2\Rightarrow 40=5u+\frac{1}{2}\times 1\times 25$
$\Rightarrow 5u=27.5\therefore u=5.5m/s$