Mechanics
Mechanics: Motion, Forces, Momentum
Mechanics on the Regents exam rewards careful attention to vectors and reference frames. Know the distinction between scalar quantities (distance, speed, mass, time) and vector quantities (displacement, velocity, acceleration, force, momentum). Average speed is total distance over total time; average velocity is displacement over time, so a round trip can have zero average velocity but nonzero average speed.
For uniformly accelerated motion, the core tools are the kinematics equations relating initial velocity, final velocity, acceleration, displacement, and time. On a velocity-time graph, slope is acceleration and area is displacement; on a position-time graph, slope is velocity. Free-fall problems use g ≈ 9.8 m/s² downward, and at the top of a vertical throw the velocity is zero while the acceleration is still g.
Newton's laws drive the force questions. Draw a free-body diagram, sum forces along each axis, and set net force equal to mass times acceleration. Static and kinetic friction use the normal force, not the weight, when a surface is inclined or an extra vertical force is applied.
Momentum is conserved in collisions when no external net force acts; kinetic energy is conserved only in elastic collisions. In perfectly inelastic collisions the objects stick together and share a common final velocity.
Worked example (rule of thumb): A ball is dropped from rest and falls 20 m. Using v² = v₀² + 2ad with a = 9.8 m/s² gives v = √(2·9.8·20) ≈ 19.8 m/s. Rule of thumb: list knowns, pick the equation missing the quantity you neither know nor want, and check sign conventions before substituting.
Traps: confusing mass with weight; forgetting that acceleration is nonzero at the peak of a throw; treating momentum as conserved when friction acts; and mixing up the slope and area interpretations of graphs.