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General SciencePhysics: Work, Energy and Power

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Which of the following correctly expresses the relationship between power, force, time and distance?

P = F/d × t

P = F × t/d

P = F × d × t

P = F × d/t

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Work, Energy and Power

Option D

P = F × d/t

Quick Summary:

Power is defined as the rate at which work is done or the rate at which energy is transferred. Mathematically, it is the ratio of work done to the time taken, and since work is the product of force and displacement, power is expressed as the product of force and velocity ( $P = F \times v = F \times \frac{d}{t}$ ).

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

If you move a box across a room, the faster you move it (covering distance $d$ in less time $t$ ), the more power you exert, regardless of the force applied.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'WDT' for Work = Distance × Time (wait, work is $F \times d$ ), then 'Power is Work per time'.

🔢 Key Formulas

$P = \frac{W}{t}$ — Definition of power as work done over time

$W = F \times d$ — Definition of work done by a constant force

$P = F \times \frac{d}{t}$ — Combined relationship of power, force, distance, and time

⚙️ Working Principle

Work is defined as $W = F \times d$ , where $F$ is force and $d$ is displacement. Power ( $P$ ) is the derivative of work with respect to time, $P = \frac{dW}{dt}$ . Since velocity $v = \frac{d}{t}$ , substituting these into the power equation yields $P = F \times \frac{d}{t}$ .

📌 Key Points

▸
Power is a scalar quantity measured in Watts ( $W$ ).
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One Watt is defined as one Joule of work per second ( $1 W = 1 J/s$ ).
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Velocity is the rate of change of displacement, so $P = F \times v$ .

✅ Advantages

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Helps in calculating the capacity of engines and motors.

❌ Disadvantages / Limitations

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Only applicable for constant forces in this simplified linear form.

🛠️ Applications / Uses

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Calculating the engine power required for a vehicle to maintain constant speed.
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Designing industrial conveyor systems.

📄 Additional Information

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The SI unit of Power is the Watt, named after James Watt.
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Option A is dimensionally incorrect as it implies $P = \frac{F \times t}{d}$ which would result in units of force/velocity.
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Option C ( $P = F \times d \times t$ ) represents Energy $\times$ time, which is not Power.

📊 Diagram / Illustration

✅

D is correct — Power is mathematically equivalent to the product of force and distance divided by the time taken, representing the rate of work done.

Core Concepts Used

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Work-Energy Theorem Definition of Power Kinematics

💡 EXAM TIP

Always perform dimensional analysis if confused: Power units are $ML^2T^{-3}$ . Substituting dimensions for $F(MLT^{-2}) \times d(L) / t(T)$ correctly yields $ML^2T^{-3}$ .

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