(i) a straight line passing through origin with slope m(ii) a straight line parallel to x axis with y intercept m

Momentum-Velocity Graph with Constant Mass
When the mass of an object remains constant, the relationship between momentum (p) and velocity (v) can be expressed as:
p = mv
- Linear Relationship:
- As velocity increases, momentum increases proportionally.
- The graph will be a straight line passing through the origin.
- Slope of the Graph:
- The slope of the line represents the mass of the object.
- A steeper slope indicates a larger mass, while a gentler slope indicates a smaller mass.
Momentum-Velocity Graph with Constant Velocity
When the velocity of an object remains constant, momentum depends solely on mass:
p = mv
- Horizontal Line:
- Since velocity does not change, momentum remains constant as well.
- The graph will appear as a horizontal line at the value of momentum corresponding to the mass and constant velocity.
- Interpretation:
- This indicates that regardless of time, the momentum does not vary when the velocity is held constant.
Conclusion
Understanding the shape of the momentum-velocity graph under varying conditions (constant mass or constant velocity) helps in visualizing the fundamental principles of motion and momentum. The linearity in the case of constant mass and the constancy in the case of constant velocity are essential concepts in physics.