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

Answer 1

The correct option is C. $5.5m/s$.

If initial velocity be $u$ and the acceleration be $a$ then the distance covered in first $5s$ will be given by the second equation of motion, $s=ut+\left(1/2\right)a{t}^2$, we get

$S_5=u\left(5\right)+\frac{a(5{)}^2}{2}=40m$........(1) (Given)

and the distance in first $10s$ will be,

$S_{10}=u\left(10\right)+\frac{a(10{)}^2}{2}$

so the distance between time $t=5s$ to $t=10$ will be

$S_5^{\prime }=S_{10}-S_5=65m$ ...........(2) (Given)

Putting corresponding values and solving the equation-1 and equation-2 we get $u=5.5m/s$.

Thus, option (C) is correct.