Question

A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. 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

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

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=5.5 m/s