Dependence of kinetic energy The kinetic energy (energy of motion) of a body __________ upon its mass and velocity.

Introduction / Context:Kinetic energy appears in collision analysis, vehicle dynamics, and energy balances. Understanding on which variables it depends is essential for predicting impact severity and designing safer systems.

Given Data / Assumptions:

• Standard translational kinetic energy model.
• Body treated as a particle (no rotation considered here).

Concept / Approach:The formula for translational kinetic energy is KE = 1/2 * m * v^2. Clearly, KE scales linearly with mass and quadratically with speed. Doubling velocity increases KE by a factor of 4, while doubling mass doubles KE. Hence KE depends on both m and v.

Step-by-Step Solution:Recall formula: KE = 1/2 * m * v^2.Inspect dependence: proportional to m; proportional to v^2.Therefore, KE depends on mass and velocity.

Verification / Alternative check:Dimensional analysis: [KE] = kg * (m^2/s^2) = N * m = J, consistent with energy units and confirming the variables that appear in the expression.

Why Other Options Are Wrong:

• “Does not depend” contradicts the explicit formula showing dependence on m and v.

Common Pitfalls:

• Underestimating the effect of speed due to the square term; small speed increases can significantly increase KE.

Final Answer:depends