I have two doubts
1) Is it a=s^5 ?
2) what's the ques. is asking?

Initial Conditions:
Given:
- Initial displacement, s = 0
- Initial velocity, v = 5 m/s

Acceleration-Displacement Relationship:
The problem states that the acceleration of the particle depends on the displacement, s, and is given by the equation a = s^5.

Determining the Equation of Motion:
To determine the equation of motion for the particle, we need to integrate the acceleration with respect to displacement. Let's solve this step by step.

- Differentiating the given equation with respect to s, we get:
da/ds = 5s^4

- Rearranging the equation, we have:
ds = da / (5s^4)

- Integrating both sides of the equation, we get:
∫ds = ∫da / (5s^4)

- Integrating the left side, we have:
s = ∫da / (5s^4)

- Integrating the right side, we get:
s = -1 / (20s^3) + C

Applying Initial Conditions:
To determine the constant of integration, C, we can apply the initial condition s = 0 when v = 5 m/s.

- Substituting s = 0 and v = 5 into the equation, we have:
0 = -1 / (20(0)^3) + C
0 = -1 / 0 + C
0 = undefined + C

- As the right side is undefined, the only possibility is that C = 0.

- Substituting C = 0 back into the equation, we have:
s = -1 / (20s^3)

Final Equation of Motion:
The equation of motion for the particle is s = -1 / (20s^3).

Explanation:
The given problem presents a scenario where the acceleration of a particle depends on its displacement. By integrating the acceleration with respect to displacement, we can determine the equation of motion for the particle. Applying the initial condition allows us to find the constant of integration, resulting in the final equation of motion. This equation describes the relationship between displacement and acceleration for the particle.

Note: The content above is a guide and may need to be modified to fit the HTML format.