Explanation
To find the distance covered when the particle next comes to rest, we need to relate acceleration (a) to velocity (v) and displacement (x).
1. Express Acceleration in terms of Velocity and Displacement:
The acceleration a can be written as:
Given that a=x−x2, we have the differential equation:
2. Integrate the Equation:
Rearranging and integrating both sides:
3. Apply Initial Conditions to find C:
The particle starts at rest at the origin, meaning at x=0, v=0.
So, the velocity equation is:
4. Find x when the particle next comes to rest:
The particle comes to rest when v=0.
Multiplying by 6 to clear fractions:
5. Solve for x:
The roots are:
Conclusion:
The particle next comes to rest after covering a distance of 23 units.
Correct Option:
C) 23
