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engine a has a greater power rating than engine b. which one of the following statements correctly describes the abilities of these engines to do work?
engine b does more work than engine a in the same amount of time
engine a and engine b do the same amount of work, engine b can do it quicker
engine a and engine b do the same amount of work, engine a can do it quicker
engine a and engine b do the same amount of work in the same amount of time

Explanation:

Step1: Recall the formula for power

Power \( P=\frac{W}{t} \), where \( W \) is work and \( t \) is time.

Step2: Analyze each option

• Option 1: If \( P = \frac{W}{t} \), for the same \( t \), higher \( P \) (engine A) means higher \( W \). So engine A does more work than engine B in the same time. This option is wrong.
• Option 2: If \( W\) is same, from \( P=\frac{W}{t}\), higher \( P \) (engine A) means lower \( t \). So engine A is quicker. This option is wrong.
• Option 3: If \( W\) is same, from \( P = \frac{W}{t}\), since \( P_A>P_B\), then \( t_A
• Option 4: If \( t\) is same, from \( P=\frac{W}{t}\), higher \( P \) (engine A) means higher \( W \). So they don't do same work in same time. This option is wrong.

Answer:

Engine A and engine B do the same amount of work, engine A can do it quicker.