In mechanics, the kinetic energy of a moving body depends on which of the following quantities?

Introduction / Context:

This question tests understanding of kinetic energy, a fundamental concept in mechanics. Kinetic energy represents the energy a body possesses due to its motion. Knowing how kinetic energy depends on mass and speed is important in physics, engineering, vehicle safety, sports science, and many everyday situations where moving objects do work or cause damage.

Given Data / Assumptions:

• The body has a certain mass m and is moving with speed v.
• Kinetic energy is defined for translational motion (straight line motion) in this context.
• We use the standard expression for kinetic energy in classical mechanics.

Concept / Approach:

In classical physics, the kinetic energy (KE) of a body of mass m moving with speed v is given by KE = (1/2) * m * v^2. This formula shows that kinetic energy is directly proportional to mass and proportional to the square of speed. Therefore, both mass and speed influence kinetic energy. Pressure is not part of this basic formula for the kinetic energy of a rigid body in translational motion.

Step-by-Step Solution:

Verification / Alternative check:

Consider two vehicles: one light and one heavy, both moving at the same speed. The heavier vehicle has more kinetic energy and can cause more damage in a collision, reflecting the dependence on mass. Now imagine the same vehicle at two different speeds. At higher speed, stopping distance and potential damage are much greater, consistent with the v^2 dependence. Practical road safety campaigns often emphasise that small increases in speed lead to much larger increases in kinetic energy, matching the formula.

Why Other Options Are Wrong:

• The velocity or speed of the moving body only: This ignores the role of mass; a heavier object at the same speed has more kinetic energy.
• The mass of the moving body only: This ignores the fact that a stationary object has zero kinetic energy; motion (speed) is essential.
• The pressure of the moving body: Pressure is not a factor in the simple particle kinetic energy formula and is irrelevant here.

Common Pitfalls:

Students sometimes mistakenly think that kinetic energy is proportional to speed, not speed squared, leading them to underestimate the effect of speed. Others may focus only on mass and assume that a heavy object always has high kinetic energy regardless of motion, forgetting that kinetic energy becomes zero if the object is at rest. Keeping the full formula KE = (1/2) * m * v^2 in mind helps to avoid these misunderstandings.

Final Answer:

Kinetic energy depends on both the mass and the speed of the moving body.