Joint Variation Word Problem: Calculating Kinetic Energy

Published on October 2, 2026

Algebra

Learn how to model joint variation, find the constant of proportionality, and calculate kinetic energy given mass and velocity. Follow step-by-step algebra work to solve for joules.

Question

For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C. View the rubric linked above for help if needed. The kinetic energy of an object, measured in joules, varies jointly with the mass of the object and the square of its velocity. Part A: Write an equation that models the kinetic energy of an object. Part B: The kinetic energy of a 10kg ball traveling 20 meters per second is 2,000 joules. What is the constant of proportionality? Show all work. Part C: How many joules of kinetic energy is generated by an 8 kg ball traveling 30 meters per second? Show all work.

Answer

Part A
Since kinetic energy ( ) varies jointly with mass ( ) and the square of velocity ( ), the equation is:
where is the constant of proportionality.
Part B
Substitute the given values , , and into the equation to solve for :
The constant of proportionality is .
Part C
Using the constant , substitute and into the equation:
The kinetic energy is joules.