Recall and use the equation for kinetic energy E_k = ½ m v^2

1.7.1 Energy – Kinetic Energy

🚀 Kinetic energy is the energy an object has because it’s moving. It’s a key concept in the Cambridge IGCSE Physics syllabus and is often asked in exams. Let’s break it down step by step!

What is Kinetic Energy?

Think of a skateboarder zooming down a hill. The faster the skateboarder goes, the more “oomph” they feel. That “oomph” is kinetic energy (KE). It’s the work that would be required to stop the skateboarder from moving.

The Formula

In physics, kinetic energy is calculated using the equation: $$E_k = \frac{1}{2} m v^2$$ where:

• $m$ = mass of the object (kg)
• $v$ = speed of the object (m/s)

Why the Square of Velocity?

The velocity appears squared because energy depends on how fast something is moving, and the relationship is not linear. If you double the speed, the kinetic energy becomes four times larger! This is a common point in exam questions, so remember it: speed squared = 4× when speed is doubled.

Quick Example

A toy car of mass $0.5\,\text{kg}$ moves at $4\,\text{m/s}$. Its kinetic energy is: $$E_k = \frac{1}{2} (0.5) (4)^2 = 0.25 \times 16 = 4\,\text{J}$$ 🎯 Result: 4 joules of kinetic energy.

Sample Calculations

Exam Tips

🎓 Key Points for the Exam:

• Always write the full formula: $E_k = \frac{1}{2} m v^2$.
• Check units: mass in kg, speed in m/s, energy in joules (J).
• Remember the velocity is squared – a quick mental trick: “double speed, quadruple KE.”
• When given mass and speed, plug them straight into the formula; no need for extra steps.
• For multiple-choice questions, look for the answer that matches the correct units and magnitude.

Practice Problems

1. A 0.8 kg ball is thrown horizontally at 5 m/s. Calculate its kinetic energy.
2. If a 1.5 kg car travels at 10 m/s, what is its kinetic energy?
3. Double the speed of a 0.4 kg object from 3 m/s to 6 m/s. By what factor does its kinetic energy change?

🔍 Tip: Work through the problems step-by-step and double-check your calculations. Practice will help you spot common mistakes like forgetting the ½ factor or squaring the speed incorrectly.