Question

Which of the following mathematical equation is correct with respect to the concept of power?

• A. Power = Time/Work done
• B. Power = Force x Distance
• C. Power = Velocity x Work done
• D. Power = Force x Velocity

Hint:

Remember: Power is the rate of doing work and can also be expressed as the product of force and velocity in the context of mechanical work.

Answer 1

The Correct Option is D

Step 1: Defining Power
Power signifies the speed at which work is performed or energy is exchanged. Quantitatively, it represents the work completed per unit of time, and is also derivable from force and velocity.
Step 2: Power Formula Derivation
The formula for power involving force and velocity is:
\[ \text{Power} = \text{Force} \times \text{Velocity} \] This arises from the relationship where work done (\(W\)) equals force (\(F\)) times distance (\(d\)), and power is the work rate: \( \text{Power} = \frac{\text{Work}}{\text{Time}} = \text{Force} \times \text{Velocity} \), with velocity being distance over time.
Step 3: Conclusion
Therefore, the accurate mathematical expression for power is (D) Power = Force x Velocity.