Unit 4.2 – Kinetic Energy

• $𝑚$ = Mass of the object (in kilograms, kg)
• $𝑣$ = Velocity of the object (in meters per second, m/s)

1. Dependence on Mass:
   Heavier objects have more kinetic energy than lighter ones if they move at the same speed. For example, a truck moving at 30 km/h has more kinetic energy than a bicycle moving at the same speed.
2. Dependence on Velocity:
   Kinetic energy depends on the square of the velocity. This means that if the speed doubles, the kinetic energy becomes four times greater! For example, a car moving at 60 km/h has four times the kinetic energy compared to when it moves at 30 km/h.
3. Units of Kinetic Energy:
   The SI unit of kinetic energy is Joule (J), just like work.

1. A rolling ball has kinetic energy because it is in motion.
2. Wind turbines generate electricity by converting the kinetic energy of moving air into electrical energy.

Quick Review, Exam Tips, Tricks & Traps

1. Kinetic energy depends on mass and the square of velocity.
2. Faster-moving objects have much higher kinetic energy due to the ${𝑣}^2$ term.
3. Kinetic energy is always positive, as both mass and velocity squared are positive values.

1. Always check the units of mass ($𝑘𝑔$) and velocity ($𝑚\mathrm{/}𝑠$). Convert them if necessary before calculating kinetic energy.
2. Remember that doubling the velocity quadruples the kinetic energy. Use this shortcut to save time in competitive exams.

1. Students often forget to square the velocity (${𝑣}^2$). Always double-check your calculations.
2. Misinterpreting the relationship between velocity and kinetic energy. For example, increasing velocity from 10 m/s to 20 m/s increases kinetic energy by a factor of 4, not 2.

1. Use proportional reasoning:
   • If velocity doubles, $𝐾𝐸$ becomes $4\times 𝐾𝐸$.
   • If mass doubles, $𝐾𝐸$ also doubles.
2. In MCQs, eliminate options where kinetic energy decreases with increasing velocity—it’s impossible unless the object stops moving.