Mechanics: kinematics and dynamics of a particle
This domain tests describing motion in one and two dimensions and explaining it with Newton's laws. Questions combine constant-acceleration formulae, projectiles, friction, connected particles and impulse-momentum.
Constant acceleration
For constant acceleration a, initial speed u and displacement s: v = u + at, s = ut + ½at², v² = u² + 2as. Fix a positive direction and keep it; use g = 9.8 m/s² unless told otherwise.
Projectiles
Resolve initial velocity into u cosθ horizontally and u sinθ vertically. Horizontal acceleration is zero, so x = u cosθ t. Vertically y = u sinθ t − ½gt² and v_y = u sinθ − gt. On level ground range R = u² sin 2θ / g, greatest at 45°.
Dynamics
Newton's second law gives F_net = ma per body. Weight is mg, reaction is perpendicular to the surface, and limiting friction is F = μR opposing impending motion. A light string over a smooth pulley has equal tension both sides. For connected particles use the system to find a, then one body to find T. Impulse J = Ft = Δ(mv); momentum is conserved along the impact line.
Worked example
A 2 kg block on a rough table (μ = 0.25) is tied over a smooth pulley to a 3 kg hanging mass. Find a and T. For the block R = 2g = 19.6 N, friction = 4.9 N. System: 3g − 4.9 = 5a, so a = 24.5/5 = 4.9 m/s². Hanging mass: 3g − T = 3a, so T = 29.4 − 14.7 = 14.7 N. Check block: T − 4.9 = 9.8, giving T = 14.7 N.
Traps
Forgetting friction opposes motion; treating tension as the hanging weight; mixing horizontal and vertical projectile components; sign errors when a direction reverses; using g = 10 when the paper expects 9.8.