Question

A particle moving rectilinearly with constant acceleration is having initial velocity of 10 m/s. After some time, its velocity becomes 30 m/s. Find out velocity of the particle at the mid point of its path?

• A. $10\sqrt{5}$ m/s
• B. $50\sqrt{5}$ m/s
• C. $60\sqrt{5}$ m/s
• D. $5\sqrt{5}$ m/s

Answer 1

The correct option is A $10\sqrt{5}$ m/s

Let total distance be $2x$

$v^2=u^2+2as$

${30}^2={10}^2+2\times a\times \left(2x\right)$

$4ax=800............\left(i\right)$

At mid point,

$v_{mid}^2={10}^2+2\times a\times x$

$4ax=2v_{mid}^2-200.............\left(ii\right)$

Subtracting (ii) from (i),

$0=1000-2v_{mid}^2$

$v_{mid}^2=500$

$v_{mid}=10\sqrt{5}m/s$