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A.3.9—Kinetic energy

Syllabus
First assessment 2025
Objective
—
Level
SL

Calculate Translational Kinetic Energy

Kinetic-energy forms

Translational kinetic energy is

Ek=12mv2=p22mE_k=\frac12mv^2=\frac{p^2}{2m}

Choose the known quantity

Use 12mv2\frac12mv^2 when mass and speed are given, or p2/(2m)p^2/(2m) when momentum is given. Kinetic energy is scalar and cannot be negative.

Worked example from local Question Bank row 35674

For m=0.14 g=1.4×10−4 kgm=0.14\,\mathrm{g}=1.4\times10^{-4}\,\mathrm{kg} and v=3.1 m s−1v=3.1\,\mathrm{m\,s^{-1}},

Ek=12(1.4×10−4)(3.1)2=6.7×10−4 J=0.67 mJE_k=\frac12(1.4\times10^{-4})(3.1)^2=6.7\times10^{-4}\,\mathrm{J}=0.67\,\mathrm{mJ}

Converting grams to kilograms before substitution keeps the energy unit in joules.

Common trap

Doubling speed quadruples kinetic energy; do not scale it linearly with speed.

A.3.9 Exam Analysis

[ 2 ]

Calculate the final speed of the car.

Retrieve the A.3 Work, Energy and Power Model

Account for energy

Define the system, identify energy stores and describe transfers. Work done by a force transfers energy; total energy is conserved even when mechanical energy is not.

Use the mechanical model

E_k= rac12mv^2,\quad \Delta E_{p,g}=mg\Delta h,\quad E_{p,elastic}= rac12k(\Delta x)^2

Conserve their sum only when resistive transfers are absent or included explicitly.

Use rates and ratios

P= rac{\Delta E}{\Delta t}=Fv,\qquad \eta= rac{E_{useful}}{E_{input}}= rac{P_{useful}}{P_{input}}

Fuel energy density connects available input energy to a chosen volume.

Final checks

Check the system boundary, signs of work and potential-energy changes, the reference height, extension from natural length, and whether the quantity is energy, power, efficiency or energy density.