A person does 1,000 J of mechanical work in 2 seconds. What is the power developed by the person?

Introduction / Context:

This straightforward numerical question is about the concept of power in physics. Power measures how quickly work is done or energy is transferred. It is commonly used for rating electrical appliances, engines, and human physical performance. Correctly using the relation between work, time, and power is a fundamental skill in basic mechanics and energy calculations.

Given Data / Assumptions:

• Work done, W = 1,000 J (joules).
• Time taken, t = 2 s (seconds).
• We assume the rate of doing work is constant over this time interval.
• We want to find power P in watts (W).

Concept / Approach:

Power is defined as the rate of doing work or the rate of energy transfer. Mathematically, P = W / t, where W is work done and t is time taken. In SI units, 1 watt is equal to 1 joule per second. By substituting the given values of work and time into this formula, we can directly calculate the power in watts.

Step-by-Step Solution:

Verification / Alternative check:

Think in terms of rates: if a device uses 500 J of energy every second, then in 2 seconds it would use 1,000 J, corresponding to a power of 500 W. This matches the numerical calculation. Everyday devices like a 500 W mixer or a 500 W heater use energy at a similar rate, making the answer physically reasonable for the amount of work described over 2 seconds.

Why Other Options Are Wrong:

• 1000 W: This would correspond to doing 1,000 J of work in 1 second, not in 2 seconds.
• 25 W and 50 W: These are much smaller power values; at 50 W, it would take 20 seconds to do 1,000 J of work, and at 25 W, even longer.

Common Pitfalls:

Students sometimes confuse power with work and pick 1,000 W simply because 1,000 J appears in the problem statement. Others may incorrectly multiply work and time instead of dividing. Some also forget that the SI unit of power is the watt and mix it up with joule. Remember the basic definition P = W / t in joules per second, and you will consistently obtain correct power values with the proper unit.

Final Answer:

The power developed by the person is 500 W.