Mechanics

Step 1: Relate kinetic energy and momentum.
The kinetic energy is related to momentum by the equation: Where: - is the momentum, - is the mass of the body. Step 2: Analyze the given condition. If the kinetic energy becomes four times its initial value: This shows that the new momentum is twice the initial momentum . Step 3: Conclusion The new momentum is twice the initial momentum. Final Answer:

Step 1: Define the frictional forces.
Frictional forces are classified into several types, including static, sliding, rolling, and kinetic friction. The maximum frictional force that resists the motion when a body just begins to slide is called limiting friction. Step 2: Conclusion.
When a body is about to move but hasn’t yet started sliding, the frictional force acting is the limiting friction. It is the maximum static friction force that can act before sliding begins. Final Answer:

Step 1: Differentiate the displacement equation to get velocity.
The displacement equation is given by: The velocity is the first derivative of displacement with respect to time: Step 2: Differentiate velocity to get acceleration.
The acceleration is the first derivative of velocity with respect to time: Step 3: Find the acceleration at
Substitute into the acceleration equation: Final Answer:

Concept: Electrical power is given by: To find maximum power, we express power in terms of a single variable and then maximize the function.
Step 1: Express current in terms of voltage .
Given:
Step 2: Substitute into power equation.

Step 3: Maximize the power function.
This is a quadratic equation: Maximum occurs at:
Conclusion:
Thus, the voltage that yields maximum power is .