Question

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

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

Answer 1

The correct option is B $25.5m{s}^{-1}$

Apply kinematic equation.

$v^2-u^2=2as$

$\Rightarrow {30}^2-{20}^2=2as\dots \dots \left(1\right)$

Apply kinematic equation, for half travel distance, (velocity at mid is $v_1$ )

$v_1^2-u^2=2a\frac{s}{2}$

$\Rightarrow v_1^2-{20}^2=as\dots \dots \left(2\right)$

From (1) and (2)

${30}^2-{20}^2=2(v_1^2-{20}^2)$

$\Rightarrow v_1^2=\frac{{30}^2-{20}^2}{2}+{20}^2=650$

$\Rightarrow v_1=25.49m{s}^{{}_{-1}}$

Velocity at mid-point is $25.5m{s}^{-1}$