Understanding the Problem
When a force acts on a body, it leads to a change in momentum over time. If the initial momentum of the body is \( p \), we need to determine the time taken to regain this momentum after experiencing a variable force.

Key Concepts
- **Newton’s Second Law**: The force acting on an object is equal to the rate of change of momentum.
- **Momentum**: Defined as the product of mass and velocity, \( p = mv \).
- **Impulse**: The change in momentum is equal to the integral of force over time, \( \Delta p = \int F dt \).

Analysis of the Force-Time Graph
- If the graph of force \( F(t) \) is provided, the area under the curve from the initial time to the time \( t \) where the body regains momentum \( p \) must equal the change in momentum.
- Assume the force varies linearly, or in segments, the areas of the shapes (rectangles, triangles) can be computed.

Calculating Time to Regain Momentum
- To regain initial momentum \( p \), the impulse delivered by the force over time \( t \) must equal the initial momentum:

• \( \int F(t) dt = p \)

- Solve for \( t \) using the specific form of \( F(t) \).

Conclusion
- The time taken \( t \) to regain momentum \( p \) depends on the area under the force-time graph, which represents the impulse. By calculating this area for the given force function, one can determine the required time.
This systematic approach ensures a clear understanding of the relationship between force, time, and momentum in dynamics.