Definition of power in mechanics Select the correct expression for power in terms of work and time.

Introduction / Context:
Power quantifies how fast work is done or energy is transferred. It is a rate, not a cumulative quantity. Correctly identifying its relationship to work and time is essential for engine sizing, electrical systems, and machine design.

Given Data / Assumptions:

• Classical definitions: work W in joules, time t in seconds.
• Average power considered; instantaneous power is dW/dt.
• Consistent SI units (watt = joule per second).

Concept / Approach:

Average power P_avg = W / t. Instantaneous power P = dW/dt. In translational motion, P = F · v, the scalar product of force and velocity, consistent with P = dW/dt since dW = F · ds.

Step-by-Step Solution:

Verification / Alternative check:

For constant force F and constant velocity v in the same direction, P = F v, which integrated over time reproduces W = P t.

Why Other Options Are Wrong:

(a), (c), (d), and (e) do not match the definition or have inconsistent dimensions.

Common Pitfalls:

Confusing energy with power; mixing average and instantaneous forms without noting the derivative.

Final Answer:

Power = work / time