Question

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?engines a and b can do the same amount of work but engine a can do it more quickly.engines a and b can do the same amount of work in the same amount of time.in the same amount of time, engine b can do more work than engine a.

Explanation:

Step1: Recall power formula

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

Step2: Analyze each option

• For the first option: If \( W_A = W_B\) (same work) and \( P_A>P_B\), from \( P=\frac{W}{t}\), we get \( t_A=\frac{W_A}{P_A}\) and \( t_B=\frac{W_B}{P_B}\). Since \( P_A > P_B\) and \( W_A = W_B\), then \( t_A
• For the second option: If \( W_A = W_B\) and \( t_A=t_B\), then \( P_A = P_B\) (from \( P=\frac{W}{t}\)), which contradicts \( P_A>P_B\).
• For the third option: If \( t_A=t_B\) and \( P_A>P_B\), from \( P=\frac{W}{t}\), we have \( W = P\times t\). So \( W_A=P_A\times t_A\) and \( W_B=P_B\times t_B\). Since \( P_A > P_B\) and \( t_A=t_B\), then \( W_A>W_B\), not \( W_B > W_A\).

Answer:

Engines A and B can do the same amount of work but engine A can do it more quickly.