The displacement `x` of particle moving in one dimension, under the action of a constant force is related to the time `t` by the equation ` t = sqrt(x) +3` where `x is in meters and t in seconds` . Find (i) The displacement of the particle when its velocity is zero , and (ii) The work done by the force in the first ` 6 seconds`.
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To solve the problem step by step, we will break it down into two parts as given in the question.
### Part (i): Find the displacement of the particle when its velocity is zero.
1. **Given Equation**: The relationship between displacement \( x \) and time \( t \) is given by:
\[
t = \sqrt{x} + 3
\]
...
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