Mechanics: Forces, Motion and Energy
Motion
Understand speed, velocity, acceleration and the difference between scalar and vector quantities. Use v = s/t and a = (v − u)/t, and interpret distance–time and velocity–time graphs: gradient of distance–time is speed; gradient of velocity–time is acceleration; area under velocity–time is displacement. A common trap is confusing distance with displacement when direction reverses, or reading the gradient of a curved graph at the wrong point. For uniform acceleration use v² = u² + 2as and s = ut + ½at².
Forces
Apply Newton's laws: balanced forces give zero acceleration; resultant force F = ma; every action has an equal and opposite reaction on a different body. Draw free-body diagrams, resolve forces, and handle friction, weight (W = mg, with g ≈ 10 N/kg) and terminal velocity. On a slope, the component of weight along the slope is mg sin θ. Remember that mass is constant but weight depends on gravitational field strength.
Moments, pressure and energy
For equilibrium, sum of clockwise moments equals sum of anticlockwise moments about a pivot; the centre of gravity matters for stability. Pressure p = F/A in pascals. Energy is conserved: kinetic (½mv²), gravitational potential (mgh) and work done (Fd) interchange, with losses to thermal energy through friction. Power P = E/t. Efficiency = useful output ÷ total input × 100%.
Worked example
A 2 kg trolley accelerates uniformly from rest to 6 m/s in 3 s. Acceleration a = (6 − 0)/3 = 2 m/s². Resultant force F = ma = 2 × 2 = 4 N. Kinetic energy gained = ½ × 2 × 6² = 36 J. Average power = 36/3 = 12 W. Check: work done = F × s, with s = ½at² = 9 m, so 4 × 9 = 36 J, confirming the energy result.