Question

A body travelling with uniform acceleration crosses two points $A$ and $B$ with velocities $20\,m{{s}^{-1}}$ and $30\,m{{s}^{-1}}$ respectively. The speed of the body at the mid-point of $A$ and $B$ is nearest to

• A. $25.5\,m{{s}^{-1}}$
• B. $25\,m{{s}^{-1}}$
• C. $24\text{ }m{{s}^{-1}}$
• D. $10\sqrt{6}\,m{{s}^{-1}}$
• E. $22\,m{{s}^{-1}}$

Answer 1

Answer: (A)

A particle moving with uniform acceleration from A to B along straight line has velocities ${{v}_{1}}$ and ${{v}_{2}}$ at A and B respectively. If C is the midpoint between A and B then velocity of the particle at C.
$v=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}}{2}}$
$=\sqrt{\frac{{{(20)}^{2}}+{{(30)}^{2}}}{2}}$
$=\sqrt{\frac{400+900}{2}}=\sqrt{650}$
$=25.5\text{ }m{{s}^{-1}}$