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

Answer: (C)

5.5 m/s

Answer 2

$\because S_{1} = ut + \frac{1}{2}at^{2}$ .....(i)

and velocity after first t sec

$v = u + at$

Now, $S_{2} = vt + \frac{1}{2}at^{2}$

$= (u + at)t + \frac{1}{2}at^{2}$ ..... (ii)

Equation

$\Rightarrow S_{2} - S_{1} = at^{2}$

$\Rightarrow a = \frac{S_{2} - S_{1}}{t^{2}} = \frac{65 - 40}{(5)^{2}} = 1\mspace{6mu} m/s^{2}$

From equation (i), we get,

$S_{1} = ut + \frac{1}{2}at^{2} \Rightarrow 40 = 5u + \frac{1}{2} \times 1 \times 25$

$\Rightarrow 5u = 27.5$ $\therefore\mspace{6mu}\mspace{6mu} u = 5.5\mspace{6mu} m/s$