Two identical blocks alide a distance D across a rough horizontal surface.as shown. Block A has an initial velocity of v_(0) and Block B has an initial velocity of (v_(0))/(2) Both blocks are still moving after sliding a distance D. Which of the following is a correct expression relating the power P_(A) generated by friction between Block A and the surface and the power P_(B) generated by friction between Block B and the surface? A (P_(A)=P_(B))=0 B (P_(A)=P_(B))gt 0 C P_(A)lt P_(B) D P_(A)gt P_(B)

Here's how to solve this problem:<br /><br />**1. Understanding Power and Work Done by Friction:**<br /><br />* Power is the rate at which work is done. The formula for power is P = W/t, where W is work and t is time.<br />* Friction always does negative work because the force of friction opposes the direction of motion.<br />* The work done by friction is given by W = -f * d, where f is the force of friction and d is the distance over which the friction acts.<br /><br />**2. Analyzing the Situation:**<br /><br />* Both blocks slide the same distance (D) across the same surface, meaning they experience the same frictional force (f).<br />* Since the initial velocity of block A is greater than that of block B, block A will take less time to travel the distance D.<br /><br />**3. Relating Power and Velocity:**<br /><br />* Since work done by friction (W) is the same for both blocks, and power (P) is inversely proportional to time (P = W/t), the block that takes *less* time will experience *greater* power from friction.<br /><br />**4. Conclusion:**<br /><br />Block A has a higher initial velocity and therefore takes less time to travel distance D. Consequently, the power generated by friction on block A (P_A) is greater than the power generated by friction on block B (P_B).<br /><br />**Therefore, the correct answer is D: *P_A > P_B***<br />