Power (Edexcel International A Level Maths: Mechanics 2)

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 t 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 a constant velocity and a constant force, the above formula can be derived by recalling the formula

                      where 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