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Work, Energy and Power

NCERT Class 11 Physics Chapter 5

Work, Energy and Power for Class 11 Physics, JEE and NEET: work-energy theorem, kinetic and potential energy, springs, energy conservation, collisions.

11 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part I (Class 11), Chapter 5 “Work, Energy and Power”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.0 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Scalar (dot) product of two vectors

    A·B = AB cos θ, projection, properties, the component formula and the angle between vectors.

    NCERT Section 5.1 11 min read 3 solved examples 7 practice questions

  2. The work-energy theorem

    Net work equals the change in kinetic energy, its derivation, braking distance and solved examples.

    NCERT Section 5.2 10 min read 3 solved examples 6 practice questions

  3. Work

    W = Fd cos θ, positive, negative and zero work, the joule and other energy units, with solved examples.

    NCERT Section 5.3 12 min read 3 solved examples 6 practice questions

  4. Kinetic energy

    K = ½mv, its link with momentum (K = p/2m), percentage changes and solved examples with practice questions.

    NCERT Section 5.4 9 min read 3 solved examples 7 practice questions

  5. Work done by a variable force

    The area under the force–displacement graph, work as an integral, and solved examples.

    NCERT Section 5.5 9 min read 3 solved examples 6 practice questions

  6. Work-energy theorem for a variable force

    The calculus proof dK = F dx, what it leaves out, and solved examples.

    NCERT Section 5.6 9 min read 3 solved examples 5 practice questions

  7. Potential energy

    Stored energy, gravitational potential energy mgh, F = −dV/dx, and conservative and non-conservative forces.

    NCERT Section 5.7 11 min read 3 solved examples 6 practice questions

  8. Conservation of mechanical energy

    K + V constant for conservative forces, a falling ball and motion in a vertical circle.

    NCERT Section 5.8 12 min read 3 solved examples 6 practice questions

  9. Potential energy of a spring

    Hooke’s law F = −kx, the work done by a spring force, V = ½kx and spring-block energy problems.

    NCERT Section 5.9 10 min read 3 solved examples 6 practice questions

  10. Power

    Average and instantaneous power, P = F·v, the watt, horsepower and kilowatt hour, with solved examples and practice.

    NCERT Section 5.10 9 min read 3 solved examples 6 practice questions

  11. Collisions

    1D formulas derived, the coefficient of restitution, 2D collisions and solved examples.

    NCERT Section 5.11 14 min read 3 solved examples 6 practice questions

Key formulas in this chapter

Scalar product

  • A·B = AB cos θ
  • A·B = Ax Bx + Ay By + Az Bz
  • i·i = 1, i·j = 0 (and the same for j and k)
  • A·A = A
  • cos θ = A·B/(AB)
  • W = F·d (work done by a constant force)

Work-energy theorem

  • Kf − Ki = Wnet
  • K = ½mv2
  • ½mv2 − ½mu2 = Fs (constant force along the motion)
  • d = K/F = mv2/(2F) (stopping distance with a constant braking force F)

Work

  • W = Fd cos θ = F·d
  • 1 J = 1 N m = 1 kg m2 s−2
  • [W] = [M L2 T−2]
  • Wnet = W1 + W2 + … (sum of the works of all the forces)
  • 1 kWh = 3.6 × 106 J, 1 eV ≈ 1.6 × 10−19 J

Kinetic energy

  • K = ½mv
  • K = p/2m
  • p = √(2mK)
  • K/K = (v/v) for the same mass

Work done by a variable force

  • W = ∫F(x)dx from xi to xf
  • ΔW ≈ F(x) Δx (one small step)
  • W = area under the F–x graph
  • W = ½kxm^2 (stretching a spring from 0 to xm)

Work-energy theorem (variable force)

  • Kf − Ki = ∫F dx from xi to xf
  • dK = F dx
  • dK/dt = mv dv/dt = Fv

Potential energy

  • V = mgh (near the Earth, h much less than the Earth’s radius)
  • F = −dV/dx
  • dV = −F dx (conservative force, one dimension)
  • ΔV = −W = −∫F dx (conservative force)
  • ½mv = mgh (body falling from rest through h)

Conservation of mechanical energy

  • Ki + Vi = Kf + Vf
  • E = K + V = constant (time-independent V; net non-conservative work zero)
  • v = √(2gH) (falling from rest through H)
  • v0 = √(5gL), vB = √(3gL), vC = √(gL) (just completing a vertical circle)
  • TA = 6mg at the bottom (just completing the circle)
  • TA − TC = 6mg (string taut, any speed)

Potential energy of a spring

  • F = −kx (Hooke’s law)
  • V = ½kx
  • Ws = ½kxi^2 − ½kxf^2
  • ½mv2 + ½kx2 = ½kxm^2
  • vm = xm√(k/m)

Power

  • P = W/t (average power)
  • P = dW/dt
  • P = F·v = Fv cos θ
  • 1 W = 1 J s, 1 mechanical hp ≈ 746 W
  • 1 kWh = 3.6 × 10 J

Collisions

  • m1v1i = m1v1f + m2v2f (momentum, m2 at rest)
  • vf = m1v1i/(m1 + m2) (completely inelastic)
  • v1f = (m1 − m2)v1i/(m1 + m2) (elastic, m2 at rest)
  • v2f = 2m1v1i/(m1 + m2) (elastic, m2 at rest)
  • ΔK = m1m2v1i^2/[2(m1 + m2)] (loss, completely inelastic)

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