P3: Mechanics, Kinematics, Dynamics, Energy and Momentum
Official Cambridge & Imperial ESAT specification requirements for Mechanics, Kinematics, Dynamics, Energy and Momentum on the Physics paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.
Official Syllabus Subtopics
Requirements specified in the UAT-UK framework
- 11D constant acceleration SUVAT equations: v = u + at, s = ut + (1/2)at², v² = u² + 2as, s = ((u+v)/2)t
- 2v–t graphs: gradient = acceleration, area under curve = displacement
- 3Newton’s laws of motion and resultant force: Fₙₑₜ = ma
- 4Coupled multi-body systems, elevators, and rope tensions
- 5Coplanar force equilibrium and resolving into perpendicular components
- 6Hooke’s law: F = kx and elastic potential energy Eₑ = ½kx² = ½Fx
- 7Spring combinations: series (1/k(eq) = 1/k₁ + 1/k₂) vs parallel (k(eq) = k₁ + k₂)
- 81D linear momentum conservation: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- 9Impulse equation: F Δt = Δp = m(v - u)
- 10Work, gravitational potential energy (ΔEₚ = mgΔh), kinetic energy (Eₖ = ½mv²), and power P = Fv
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
For coupled multi-body systems (like tied blocks or train carriages), treat the entire assembly as a single composite mass to find acceleration in 1 line.
Identical springs in series halve overall stiffness (k/2), while parallel springs double overall stiffness (2k).
Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.
Tested Topics in Specification P3
Master the individual question patterns and Sub-90 shortcuts for this specification.
1D Multi-Stage Kinematics (v–t Graph Areas/Gradients) & Constant-Acceleration SUVAT
Never use algebraic SUVAT if a v-t sketch gives a triangle/trapezium: displacement is simply average velocity (u+v)/2 * t. Always use g = 10 N/kg for vertical free-fall.
1D Coupled Multi-Body Resultant Force (Fₙₑₜ = ma), Lifts & Internal Tension
Two-line coupled-body rule: Line 1 (Whole System) a = F(net, total) / (m1 + m2). Line 2 (Trailing Body only) T - F(drag, 2) = m2 * a. If resistive force is proportional to mass, tension split is purely T = F(drive) * m(rear) / (m1 + m2).
Equilibrium of Coplanar Forces, Drag/Terminal Velocity Balancing & Tension-Spring/Pulley Systems
In static or dynamic equilibrium (at rest or constant terminal velocity), net force in every direction is zero: upward tension/drag balances downward weight (T = mg or F(drag) = mg), and pulley rope tension is uniform throughout a frictionless massless cord.
Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx²)
Spring stiffness behaves OPPOSITE to resistors: two identical springs in parallel are stiffer (k(eff) = 2k, half the extension); in series they are softer (k(eff) = k/2, double the extension). Always compute x = |L - L₀| first.
1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions
Draw a (+) arrow on the page before writing a single number: rebounding off a wall ALWAYS gives |Δp| = m(|v| + |u|), and kinetic energy relates to momentum via Eₖ = p² / (2m).
Work-Energy-Power Conservation (ΔEₚ = mgΔh, Eₖ = ½mv²) & Resistive Drag Work
Write the Master Energy Accounting line: E(k, initial) + mgh(initial) = E(k, final) + mgh(final) + F(drag) * d (with g = 10 N/kg). For constant velocity v against drag F, Mechanical Power is simply P = F * v.
Ready to Master Specification P3 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.