1. Centre of mass of particles, calculating the position of the centre of mass and solving for unknown constants. 2. Force and motion analysis of a car towing a trailer, calculating the power required for constant speed and applying the work-energy principle to find distances. 3. Impulse and velocity analysis, determining the particle′s velocity and the possible values of impulse. 4. Acceleration and position vector calculations for a particle, using time-dependent velocity and solving for position at specific times. 5. Collision dynamics and restitution, calculating velocities after direct collisions and finding the coefficient of restitution. 6. Mechanics of a ramp and friction, calculating work done against friction, using work-energy principle to find initial speed, and determining time and angle during projectile motion.