A particle falls freely from rest through a distance d. Its speed is then; A coconut falls from a 12 m tree. What would be its velocity half-way down?

The particle falls from rest, so the initial velocity $u = 0$.
The distance fallen is $s = d$.
The acceleration due to gravity is $a = g$.
We need to find the final speed $v$.
The kinematic equation relating these variables is $v^2 = u^2 + 2as$.

Since speed is a scalar quantity and always positive, we take the positive square root.

Comparing this with the given options, the correct option is B.

The final answer is $\boxed{\text{B. } \sqrt{2gd}}$.

Total height of the tree $H = 12 \, \text{m}$.
The coconut falls from rest, so initial velocity $u = 0$.
We need to find the velocity when it is half-way down.
Distance fallen $s = \frac{H}{2} = \frac{12 \, \text{m}}{2} = 6 \, \text{m}$.
Acceleration due to gravity $g = 9.8 \, \text{m/s}^2$.

Substitute the values:

The calculated velocity $10.84 \, \text{m/s}$ is closest to $11 \, \text{m/s}$.

The final answer is $\boxed{\text{B. } 11 \, \text{m/s}}$.