if displacement of a particle is directly proportional to square root of time the acceleration is proportional to

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

Explore how acceleration is determined in proportional motion problems where displacement is directly proportional to the square root of time. Learn about velocity and acceleration formulas and their applications. Suitable for high school students.

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