Average and Instantaneous Power
Power is the rate of doing work, Pavg = W/t and Pinst = F.v, measured in watts.
What is Average and Instantaneous Power?
The SI unit of power, equivalent to one joule of work performed per second.
Key formula / rule: Average Power
Key points
- Distinguish between average and instantaneous rates of work.
- Apply the dot product formula to solve multi-dimensional power problems.
- Relate power to kinetic energy changes using the Work-Energy Theorem.
Common exam trap
Confusing kWh (energy) with kW (power).
Definitions
- Term
Watt
- Meaning
The SI unit of power, equivalent to one joule of work performed per second.
- Term
Efficiency
- Meaning
The ratio of useful work performed by a system to the total energy consumed.
Learning objectives
Distinguish between average and instantaneous rates of work.
Apply the dot product formula to solve multi-dimensional power problems.
Relate power to kinetic energy changes using the Work-Energy Theorem.
Formulae
- Name
Average Power
- Note
Total work done over total time.
- Expression
Pavg = ΔW / Δt
- Name
Instantaneous Power (Vector form)
- Note
F is the force vector and v is the velocity vector.
- Expression
P = F · v
- Name
Power in terms of Kinetic Energy
- Note
Rate of change of kinetic energy equals net power.
- Expression
P = dK/dt
Prerequisites
Dot product of vectors
Basic differentiation
Definition of Work (F.s)
Common mistakes
Confusing kWh (energy) with kW (power).
Forgetting to include the cos(θ) term in P = Fv.
Using total time for instantaneous power calculations instead of the derivative.
Keywords
Watt
Dot Product
Work-Energy Theorem
Horsepower
Scalar
Practice preview
A machine does 30,000 Joules of work in 1 minute. What is the average power delivered by the machine?…
easy
An engine pumps 400 kg of water through a height of 10 m in 40 seconds. If the efficiency of the engine is 80%, what is the input power required? (Take g = 10 m/s²)…
medium
A vehicle of mass 'm' starts from rest and accelerates such that the instantaneous power delivered to the vehicle has a constant magnitude P. The instantaneous velocity of the vehicle as a function of time 't' is proport…
hard