Power (CIE A Level Maths: Mechanics)

What is power?

• Power is developed as an engine or machine does work
• Power is the rate of doing work, usually by the driving force of an engine
  • It is the same as work done per second
  • The work done is converting fuel (a type of chemical energy) into a driving force
• In your Mechanics A Level course, power will usually be in questions about moving vehicles
• Power is a scalar quantity and can only take a positive value

How is power calculated?

• Power is the rate of doing work and can be calculated by the formula

Where WD is the work done by the driving force in Joules and is the time in seconds

• If a driving force, F N, is acting on an object moving with velocity, v m s^-1 then power can be calculated using the formula

• • The velocity must be in the same direction as the force
  • For constant and the above formula can be derived by recalling the formula

                      where v is speed or velocity and is distance or displacement.

• • The derivation can also be shown for a constant force, F N and considering the rate of doing work over a very small interval of time
    • 
    • As the time δt gets smaller and approaches  then
    •  

• The units for power are watts (W) or kilowatts (kW)
  • 1 watt = 1 joule per second
  • 1 kilowatt = 1000 watts

How is power used in calculating maximum speed?

• As a vehicle gains speed the driving force can decrease to create the same amount of power
• If the vehicle maintains maximum power its driving force will decrease as its speed increases and it will eventually reach a point where its resultant force is zero (the driving force will balance the resistance forces)
  • When the resultant force becomes zero, by Newton’s Second Law, acceleration will also become zero and the vehicle will be travelling at maximum speed
  • The maximum power output of a vehicle can be found when the vehicle is moving at its maximum speed and the acceleration is zero
  • If the maximum power output is known, then maximum speed can be found when the vehicle is travelling at its maximum power with zero acceleration and the resultant forces are balanced