Question

A body is moving with constant acceleration from A to B in a straight line. C is the mid-point of AB. If u and v are the speeds at A and B respectively. The speed at C is

• A. $\frac{u+v}{2}$
• B. $\frac{uv}{2}$
• C. $\sqrt{\frac{u^2+v^2}{2}}$
• D. $\sqrt{\frac{u^2-v^2}{2}}$

Answer 1

Answer: (C)

$\sqrt{\frac{u^2+v^2}{2}}$

Given that body is moving with constant acceleration.

Lat the total distance $AB$ be $2x$ and the acceleration be $a$.

$\Rightarrow AC=BC=x$

Speed at $A$ is $u$ and speed at $B$ is $v$.

Let the speed at $C$ be $z$.

$\Rightarrow z^2=u^2+2ax$ and $v^2=z^2+2ax$

$\Rightarrow z^2-u^2=v^2-z^2$

$\Rightarrow 2z^2=u^2+v^2$

$\Rightarrow z=\sqrt{\frac{u^2+v^2}{2}}$