In basic mechanics, which of the following situations clearly results in an increase in power output, assuming work is measured in the same units?

Introduction / Context:
Power is a fundamental quantity in physics and engineering that tells us how quickly work is done or energy is transferred. It is not enough to know how much work is done; we must also know how long it takes. This question tests your understanding of the definition of power and asks you to select the scenario that clearly leads to a higher power output compared with alternatives.

Given Data / Assumptions:

• Work is measured in joules or an equivalent energy unit.
• Time is measured in seconds or minutes, but we consider only relative changes.
• Power is defined as work done divided by the time taken.
• Each option describes a qualitative change in work and time.

Concept / Approach:
By definition, power P is given by P = W / t, where W is the work done and t is the time taken. To increase power, we can either increase the work done while keeping time the same, decrease the time while keeping work the same, or both increase work and decrease time in a favourable way. Among the scenarios given, doing more work in less time clearly increases the numerator and reduces the denominator, resulting in a larger value of P than before. Doing less work or taking more time generally reduces power.

Step-by-Step Solution:
Step 1: Write the power formula P = W / t.Step 2: Consider scenario A: more work means larger W, and less time means smaller t, so W / t becomes larger; power increases.Step 3: Consider scenario B: less work (smaller W) and more time (larger t) both act to reduce W / t, lowering power.Step 4: Consider scenario C: less work and less time together; the net effect on power is uncertain without numbers, but generally less work suggests less power unless time is much shorter.Step 5: Consider scenario D: more work and more time; again the net effect is unclear, but extra time may reduce the advantage of more work.Step 6: Identify scenario A as the only option that clearly and unambiguously increases power compared with doing the same work in more time.

Verification / Alternative check:
Think of two people climbing a staircase of the same height. If person 1 climbs in 10 seconds and person 2 climbs in 5 seconds, both doing the same work against gravity, person 2 develops twice the power because the same work is done in half the time. If someone carries a heavier load up the same stairs in even less time, they develop even more power. These everyday examples confirm that more work completed in less time corresponds to higher power.

Why Other Options Are Wrong:
Doing less work in more time obviously decreases power, because both W decreases and t increases. Doing less work in less time could still result in less power if the reduction in work is significant; the option is ambiguous but clearly does not guarantee higher power. Doing more work in more time may or may not increase power depending on the relative changes; the option does not clearly state that power increases. Only more work in less time gives a definite increase.

Common Pitfalls:
Some learners confuse power with work or energy and may think that any increase in work automatically means more power, ignoring the role of time. Others may focus only on time and forget that reducing time without considering work done is not the whole story. To avoid these mistakes, always apply P = W / t and think about what happens to both W and t.

Final Answer:
Power clearly increases when more work is done in less time.