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Kinetic Energy (Oxford AQA IGCSE Physics)

Revision Note

Leander Oates

Expertise

Physics

Kinetic Energy

  • Energy in the kinetic store is defined as:

The amount of energy an object has as a result of its mass and speed

  • This means that any object in motion has energy in its kinetic store

    • If an object speeds up, energy is transferred to its kinetic store

    • If an object slows down, energy is transferred away from its kinetic store

Kinetic energy of a moving car

Kinetic Energy Car, for IGCSE & GCSE Physics revision notes
A moving car has energy in its kinetic store

  • The amount of energy in an object's kinetic store can be calculated using the equation:

Ek = ½ × m × v2

  • Where:

    • Ek = kinetic energy in joules (J)

    • m = mass of the object in kilograms (kg)

    • v = speed of the object in metres per second (m/s)

  • The equation tells us that if the mass of an object is doubled for a given speed, then its kinetic energy will double

    • This is because kinetic energy is directly proportional to mass

    • E subscript k space proportional to space m

  • If the speed of the object is doubled for a given mass, it will have four times the kinetic energy

    • This is because kinetic energy is directly proportional to velocity squared

    • E subscript k space proportional to space v squared

Worked Example

Calculate the energy in the kinetic store of a vehicle of mass 1200 kg moving at a speed of 27 m/s.

 Answer:

Step 1: List the known quantities

  • Mass of the vehicle, m = 1200 kg

  • Speed of the vehicle, v = 27 m/s

Step 2: Write down the equation for kinetic energy

EK = ½ × m × v2

Step 3: Calculate the kinetic energy

EK = ½ × 1200 × (27)2

EK = 437 400 J

Step 4: Round the final answer to 2 significant figures

EK = 440 000 J

Worked Example

A car of mass 1500 kg is travelling at 13 m/s (30 mph).

a) Show that if the speed of the car is doubled, the kinetic energy of the car is increased by a factor of 4.

b) Use your answer to explain why obeying speed limits on residential roads is important to the safety of pedestrians.

Answer:

Part a)

Step 1: List the known quantities

  • Mass, m space equals space 1500 space kg

  • Speed, v space equals space 13 space straight m divided by straight s

Step 2: Write out the kinetic energy equation

K subscript E space equals space 1 half space cross times space m space cross times space v squared

Step 3: Determine the kinetic energy of the car at 13 m/s

K subscript E space equals space 1 half space cross times space 1500 space cross times space open parentheses 13 close parentheses squared

K subscript E space equals space 126 space 750 space straight J

Step 4: Determine the kinetic energy of the car if the speed is doubled

K subscript E space equals space 1 half space cross times space 1500 space cross times space open parentheses 13 space cross times space 2 close parentheses space squared space

K subscript E space equals space 1 half space cross times space 1500 space cross times space open parentheses 26 close parentheses squared

K subscript E space equals space 507 space 000 space straight J

Step 5: Show that the kinetic energy of the car has increased by a factor of 4

fraction numerator 507 space 000 over denominator 4 end fraction space equals space 126 space 750 OR 126 space 750 space cross times space 4 space equals space 507 space 000

  • The car has a kinetic energy of 126 750 J when travelling at a speed of 13 m/s, when the speed is doubled to 26 m/s the kinetic energy is increased by a factor of 4 to 507 000 J

Part b)

  • The faster a car is travelling the more energy it has in its kinetic store

  • For the car to come to a sudden stop (for example, if a pedestrian steps into the road), the energy in its kinetic store must be transferred by heating to the thermal store of the breaks

  • Since kinetic energy is proportional to the speed squared, even small increases in speed will have a large impact on the car's stopping distance

  • If the car is travelling too fast to be able to stop before hitting a pedestrian, some of the kinetic energy of the car will be transferred to the pedestrian upon impact

  • The greater the speed of the car at the point of collision, the greater the energy transferred and the more severe the injury

Exam Tip

When performing calculations using the kinetic energy equation double-check that you have squared the speed. Forgetting to do this is the most common mistake that students make.

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    Leander Oates

    Author: Leander Oates

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.