Select the correct answer. Which equation correctly relates kinetic energy, mass, and velocity? A. B. C. D.
The Correct Answer and Explanation is:
The correct equation that relates kinetic energy (KE), mass (m), and velocity (v) is:
KE = ½mv²
✅ Correct Answer: KE = ½mv²
🔍 Explanation
Kinetic energy is the energy an object has due to its motion. The faster an object moves or the more massive it is, the more kinetic energy it possesses. The formula that expresses this relationship is:
Kinetic Energy (KE) = ½ × mass (m) × velocity² (v²)
This formula shows that kinetic energy depends on both the mass of the object and the square of its velocity. This means:
- If the mass doubles, kinetic energy also doubles.
- If the velocity doubles, kinetic energy increases by four times (because velocity is squared).
📘 Where does the formula come from?
The formula is derived from work-energy principles in physics. Work is defined as a force applied over a distance. When a force accelerates an object from rest to a certain velocity, the work done on the object becomes its kinetic energy.
Using Newton’s second law (F = ma) and basic kinematic equations, you can derive the kinetic energy formula:
- Work = Force × distance
- Force = mass × acceleration
- From kinematics: v2=u2+2adv^2 = u^2 + 2adv2=u2+2ad
(If starting from rest, u=0u = 0u=0, so v2=2adv^2 = 2adv2=2ad) - Solve for distance: d=v2/(2a)d = v^2 / (2a)d=v2/(2a)
- Substitute into Work:
Work = F × d = ma × (v² / 2a) = ½mv²
So, kinetic energy is the work done to bring an object to its current speed, and is captured in the equation:
KE = ½mv²
This equation is widely used in physics, engineering, and mechanics to calculate how much energy a moving object has.
