PYQ Vault

Playbook

Work, Energy and Power

The work-energy theorem, power and collisions. Energy conservation usually beats a force analysis.

Questions in the bank
123
q/paper in 2025–26
0.79
Numeric answer
29%
Notes pages
6

Tier: Long tail

When you’ll see it

A speed after a force has acted over a distance, a spring compressed, a collision or an explosion, or a rate of doing work.

How this chapter is tested

Most questions are short: one energy balance or one momentum balance, then a line of arithmetic. The marks go to choosing the right balance.

The work-energy theorem always holds, as long as every force's work is counted with its sign. Momentum survives every collision and explosion. Kinetic energy survives only an elastic collision, and mechanical energy only where no friction or impact takes any away.

This is a long-tail chapter, and it is often set as a numeric-answer question. The bullet-and-pendulum shape is the standard test of the order: momentum through the impact, energy through the swing.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Work by constant and variable forces

    W = F·s for a constant force; the integral of F dx, or the signed area under an F–x graph, when it varies with position.

  • Work-energy theorem and K = p²/2m

    The total work of all forces is the change in kinetic energy; for one body, p multiplied by n makes K multiplied by n².

  • Potential energy and mechanical energy

    F = −dU/dx; a spring stores ½kx²; where only conservative forces work, kinetic plus potential energy stays constant.

  • Power

    P = F·v at an instant; under constant power the force falls as the speed rises and x grows as t^(3/2).

  • Impulse, explosions and sticking collisions

    Impulse is the change in momentum; momentum is conserved in an explosion, a recoil or a sticking collision, and kinetic energy is not.

  • Elastic collisions and restitution

    Elastic means momentum and kinetic energy both conserved; e compares separation speed with approach speed, and a bounce height goes as e².

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Energy conserved through an impact

    ½mu² = (M + m)gh skips the impact. Use momentum for the impact, then energy for the swing.

  • Spring energy written as kx²

    The stored energy is ½kx², and between two stretches it is ½k(x₂² − x₁²), each measured from the natural length.

  • Height goes with e, not e²

    A ball leaving the floor at e times its arrival speed rises to e² times its starting height, and every bounce is travelled twice.

  • Constant power taken as constant force

    Using v = at and x = ½at² gives x ∝ t². Under constant power x ∝ t^(3/2).

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Work, Energy and Power notes

Drill every Work, Energy and Power question

123 questions from the bank, across 6 subtopics.

Drill the 123 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

Related playbooks

Often paired with this one — the technique or the trap overlaps. Drill these next.