Given that the displacement $s$ of a particle is directly proportional to the square root of time $t$, we can express this relationship as:

$s = k \sqrt{t}$

where $k$ is a constant of proportionality.

To find the relationship of acceleration with respect to time, we need to derive the expressions for velocity and acceleration.

1. Velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{ds}{dt} = \frac{d}{dt} (k \sqrt{t})$ Using the power rule for differentiation: [ v = k \cdot