Kinetic Energy (Cambridge (CIE) AS Physics)

Derivation of KE = 1/2mv²

• Kinetic energy is energy an object has due to its motion (or velocity)

• Resultant forces make objects accelerate as described by Newton's second law F = ma

• Work is done by that force and energy is transferred to the object

• Using this concept of work done and an equation of motion, the extra work done due to an object's speed can be derived

• Consider a mass, m, at rest which accelerates to a velocity, v, over a displacement, s

• The work done in accelerating the mass is:

• Newton's Second Law states that:

• The suvat equation for velocity is:

  

  • If the initial velocity is zero, u = 0

  • And displacement, s 

  • Then:

    

  • Rearranging to make a the subject:

• Substituting this expression for a into Newton's Second Law gives:

• Substituting this expression for F into the work done equation gives:

• The mass is now able to do extra work due to its speed

  • The amount of extra work is equal to 

• The mass now has: 

Kinetic energy

• The faster an object is moving, the greater its kinetic energy

• When an object is falling, it is gaining kinetic energy since it is gaining speed

• This energy transferred from the gravitational potential energy it is losing

• An object will maintain this kinetic energy unless its speed changes

• The amount of kinetic energy an object has is determined by its mass and its speed:

• Where:

  • E_k = kinetic energy in joules (J)

  • m = mass in kilograms (kg)

  • v = velocity in metres per second (m s^-1)

A car travelling forwards

Kinetic energy is the energy an object has when it is moving, determined by its mass and its speed