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CAIE A-Level Physics 5.2.3 Deriving the Kinetic Energy Formula

Practise deriving kinetic energy from work, Newton’s second law and constant-acceleration equations, showing algebra, conditions and units.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • derive EK = 1/2 mv² from the equations of motion and the work–energy relationship
  • show the algebraic link between force, displacement, acceleration and change in kinetic energy
  • check the conditions and units used in the kinetic-energy derivation

5.2.3—The equations of motion, the formula for kinetic energy EK = 1/2 mv2 question 1

[Maximum number: 1]

A student attempts to derive the formula for kinetic energy EKE_{\mathrm{K}}. She begins by considering an object of mass m which is initially at rest. A constant force F applied to the object causes it to accelerate to final velocity v in displacement s. The kinetic energy gained by the object is equal to the work done on the object by the force F.

Which equation would the student not need in order to derive the formula for EKE_{\mathrm{K}} ?

A

F=m a

B

W=F s

C

E=12FsE=\frac{1}{2} F s

D

v2=u2+2asv^{2}=u^{2}+2 a s

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