1. Acceleration and Position Vector: Using the given position vector of a particle to find its acceleration at a specific time.

2. Energy and Time Analysis: Calculating time intervals for a particle’s motion and determining the necessary speed to return to the starting point.

3. Impulse and Velocity: Using impulse and the change in velocity to find the two possible values of velocity for a particle after receiving an impulse.

4. Work-Energy Principle on a Truck: Solving for the resistance force in a truck’s motion, including the use of energy and deceleration parameters.

5. Tension and Coefficient of Friction: Finding the tension in a string supporting a rod and determining the coefficient of friction at the contact point.

6. Kinematic and Energy Equations: Solving for speed, energy, and horizontal distance in a projectile motion problem involving gravity and friction.