Physics - Mechanics, Motion, Forces, Work and Energy
This domain tests how well you describe motion with graphs and equations, draw force diagrams, and apply energy conservation to carts, pendulums, and simple machines. Aichi entrance items usually pair a calculation with a qualitative explanation, so write units and directions explicitly.
Motion
Speed = distance ÷ time; velocity adds direction. Acceleration = change in velocity ÷ time. For uniform acceleration: v = u + at, s = ut + ½at², and v² = u² + 2as. On a distance–time graph the slope is speed; on a velocity–time graph the slope is acceleration and the area is displacement. Average speed uses total distance ÷ total time, not the mean of two speeds unless acceleration is uniform.
Forces
Newton's first law: zero net force means constant velocity, including rest. Second law: F = ma. Third law: action and reaction are equal, opposite, and act on different bodies. Weight = mg, normal force is perpendicular to a surface, friction opposes relative sliding, and tension acts along a string. Resolve sloped forces into components parallel and perpendicular to the surface.
Work and energy
Work W = Fs cos θ; power P = W/t. Kinetic energy = ½mv²; gravitational potential energy = mgh. Mechanical energy is conserved when only gravity or springs do work; friction transfers energy to thermal. Efficiency = useful output ÷ input.
Worked example
A 4.0 kg cart starts from rest and is pushed 3.0 m by a horizontal 10 N force against 4.0 N friction. Net force = 6.0 N, so a = 1.5 m/s². Net work = 6.0 × 3.0 = 18 J. Using v² = 2as = 9.0, v = 3.0 m/s. Check: ½ × 4.0 × 3.0² = 18 J.
Traps
Do not confuse mass with weight. Zero velocity does not imply zero acceleration at a turning point. A force perpendicular to motion does no work. Include friction with the correct sign. Reaction forces do not cancel because they act on different objects.